m*f
发帖数: 8162 | 1 我想的是错的sigh...
看来要对第二基本型在v0, v1方向上作偏导，搞到三维tensor了，sigh... |
|
l********e
发帖数: 3632 | 2 ArXiv. Peterson, Wilhelm
AN EXOTIC SPHERE WITH POSITIVE SECTIONAL CURVATURE
继去年1/4 pinched sphere theorem以后的一个重大突破
希望是真的！ |
|
j*******e
发帖数: 349 | 3 我手上有一本日本人写的微积分教材, 一个老教授退休送的,说他看不懂,留给我做个纪
念,前后有些破损, 估计他以为中国人都懂日文,是东京工业大学的教材,昭和元年出版,
我查了一下是1926, 里面的内容很丰富, 以微积分I的内容为主,还有一些微积分2,3的
内容,包括多元积分,曲面,曲线,还有curvature之类的,但是内容有点象国内的数学分析
,绝对比老美一般的微积分I教材难,除了纸黄了些,印刷绝对工整,还是用线装的,真不知
道那个老教授从那里弄的. |
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w**a
发帖数: 1024 | 4 一个解析函数f(z), 在某点z0 有 f'(z=z0)=0.
我们知道 z0是一个鞍点。怎么证明在这一点的
Gaussian curvature < 0 啊？ 谢谢高手 |
|
w**a
发帖数: 1024 | 5 f(z) is analytical function of complex variable z, z = x + i*y, i = \sqrt(-1)
let the real part be u(x,y) = Re[f(z)].
the metric is normal Euclid distance in 3D space.
the surface of real part is parametrized as (x,y, u(x,y))
prove: the Gauss curvature is <= 0 at point z0 where f'(z=z0) =0. |
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c****e
发帖数: 2097 | 6 you need the local radii of curvature in terms of z. |
|
PT
发帖数: 148 | 7 A question puzzles me.
For a cubic curve
y(x) = ax^3 + bx^2 + cx + d
we want to find the inflexion point.
We differentiate the equation with respect to x twice to obtain
y'' = 6ax + 2b
Since at inflexion point, curvatures change signs, i.e. y'' = 0.
then
6ax + 2b = 0 ----> x = -b/(3a)
which means we have only one inflexion point for cubic curves.
However, in a website, it is said for cubic Bezier curves, there are at most
two inflexion points.
Why is that?
Thank you. |
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s**e
发帖数: 1834 | 8 not sure whether your "hyper-sphere" already includes hyperbolic space,
which has negative curvature. |
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R********n
发帖数: 519 | 9 hyperbolic space，双曲空间？~~这个没有考虑到
那，比如在2 D的Euclidean space，所有的global constant curvature curve，就是
circle(部分circle也包括了)和hyperbolic curve？
Thanks |
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s**e
发帖数: 1834 | 10 Hyperbolic space (双曲空间) has curvature -1, but not nessecarily can be
embeded in an Euclidean space. Some info about hyperbolic space:
http://en.wikipedia.org/wiki/Hyperbolic_space
I suppose the "hyperbolic curve" in your post refers to the curve x^2-y^2=1
in a Euclidean space. For some subtle reasons, it is NOT the same thing defined in the above wiki link, though they are defined using the same equation.
In the wiki link, a n-dim hyperbolic space is defined in a (n+1)-dim Minkowski space (not a |
|
l********e
发帖数: 3632 | 11 曲率如果只截面曲率（sectional curvature）那么只有三种
K=1的是球面，包括高维球面，或者他们的商空间，比如透镜空间(lens space，prizm
manifold等）
K=1的是欧式空间，或者它的商空间，比如环面，或者克莱因瓶等
K=-1的是双曲空间\mathbb H^n，或者它的商空间。
最后如果流行是联通的，那么局部常值和整体常值是一个意思。
如果你指的是其他曲率比如Ricci曲率，就复杂了。 |
|
F*******n
发帖数: 8 | 12 The following is copied from p.622 of Siu's 1988 Annals paper "The Existence
of Kahler-Einstein...". Siu is really angry at Tian's plagiarism.
Added after submission of paper. I presented the results and methods of this
paper in the Geometry and Analysis Conference at Columbia University in
April, 1986. G. Tian in August, 1986 wrote a paper "On Kihler-Einstein
metrics on certain Kihler manifolds with cl(M) > 0" (Invent. Math. 89 (1987)
, 225-246) in which he constructed Kdhler-Einstein metrics f... 阅读全帖 |
|
v*********n
发帖数: 573 | 13 田院士曰：“窃idea不算偷”。
The following is copied from p.622 of Siu's 1988 Annals paper "The Existence
of Kahler-Einstein...". Siu is really angry at Tian's plagiarism.
Added after submission of paper. I presented the results and methods of this
paper in the Geometry and Analysis Conference at Columbia University in
April, 1986. G. Tian in August, 1986 wrote a paper "On Kihler-Einstein
metrics on certain Kihler manifolds with cl(M) > 0" (Invent. Math. 89 (1987)
, 225-246) in which he constructed Kdhler-... 阅读全帖 |
|
l********e
发帖数: 3632 | 14 我仔细想了想，还真不知道Differential Geometry到底是研究什么的。
我能想到的就是Differentiable manifold, differentiable maps, tangent bundle,
affine connection, curvature tensor等。再有其他东西就算其他比如Differential
topology or Riemannian geometry之类的研究对象了。
所以上述这些科目的参考书中都会有相应的微分几何的介绍。
比如do Carmo Riemannian geometry中就有不错的介绍。他的特点是书写得很几何化，
不是那么抽象。Burcker 写的Introduction to Differential Topology也可以作为入
门。还有Helgason 的名著Differential Geometry Lie Groups and Symmetric Spaces
中也有介绍。所以单独的微分几何书并不是很有趣，有趣的是当微分几何应用到其他领
域中的时候。
如果偏爱中文，白正国,沈一兵的Riemann几何初步或... 阅读全帖 |
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D******g
发帖数: 125 | 15 来自主题: Mathematics版 - 一个牛人 这人很牛啊， 又是个8页的强文
arXiv:1108.1888 [pdf, ps, other]
3-manifolds with nonnegative Ricci curvature
Gang Liu
Comments: Revised version, accepted by Inventiones Mathematicae
Subjects: Differential Geometry (math.DG) |
|
M****o
发帖数: 4860 | 16 他应该也不止三篇paper，只是这三篇是得奖原因吧
The entropy formula for the Ricci flow and its geometric applications
G Perelman - arXiv preprint math/0211159, 2002 - arxiv.org
Abstract: We present a monotonic expression for the Ricci flow, valid in all
dimensions and without curvature assumptions. It is interpreted as an
entropy for a certain canonical ensemble. Several geometric applications are
given. In particular,(1) Ricci flow, ...
Cited by 1079 Related articles All 39 versions Cite [PDF] from arxiv.org
Ricci f... 阅读全帖 |
|
B****n
发帖数: 11290 | 17 我覺得像
無理數 (超越數)
elements(原典)裡公理化的描述
極限 微分和積分
Gaussian curvature是intrinsic
以及像非歐幾何(沒有第五平行公設)...
這些概念對世界都有很大的影響
? |
|
D******g
发帖数: 125 | 18 Mathematics of the USSR-Sbornik Volume 67 Number 2
N M Ivochkina 1990 Math. USSR Sb. 67 317 doi:10.1070/SM1990v067n02ABEH002089
SOLUTION OF THE DIRICHLET PROBLEM FOR CURVATURE EQUATIONS OF ORDER $ m$ |
|
D******g
发帖数: 125 | 19 Ivochkina, N. M. The Dirichlet problem for the curvature equation of order m
. (Russian) Algebra i Analiz 2 (1990), no. 3, 192--217; translation in
Leningrad Math. J. 2 (1991), no. 3, 631–654
多谢拉!! |
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g****a
发帖数: 1520 | 20 田肯定是抄了。田是听说了Donaldson他们已经接近于证明Yau猜想，才突然杀出来的，
Donaldson与合作者近几年来一直在推进这个问题，try了各种不同方法。田根本毫无贡
献，上一次有贡献是1997年那篇positive scalar curvature的文章。
如果搞一个committee来评判一下，田肯定完蛋。其实Donaldson都已经鉴定过了。
10 |
|
g****a
发帖数: 1520 | 21 田肯定是抄了。田是听说了Donaldson他们已经接近于证明Yau猜想，才突然杀出来的，
Donaldson与合作者近几年来一直在推进这个问题，try了各种不同方法。田根本毫无贡
献，上一次有贡献是1997年那篇positive scalar curvature的文章。
如果搞一个committee来评判一下，田肯定完蛋。其实Donaldson都已经鉴定过了。
10 |
|
x********i
发帖数: 905 | 22 Simon Brendle Receives 2014 AMS Bôcher Prize
Monday December 2nd 2013
Providence, RI
Simon BrendleSimon Brendle (pictured at left), professor of mathematics at
Stanford University, is receiving the 2014 AMS Maxime Bôcher Memorial
Prize. Presented every three years by the American Mathematical Society, the
Bôcher Prize recognizes an outstanding research paper in the field of
mathematical analysis that has appeared in the preceding six years. The
prize will be awarded on Thursday Ja... 阅读全帖 |
|
o****i
发帖数: 23 | 23 谢谢comment. 我看到有文章研究往constant sectional curvature的Riemannian
manifold嵌入，那又太特殊了。
欧式空间没法保证graph metric的等距嵌入。 |
|
o****i
发帖数: 23 | 24 谢谢comment. 我看到有文章研究往constant sectional curvature的Riemannian
manifold嵌入，那又太特殊了。
欧式空间没法保证graph metric的等距嵌入。 |
|
D******g
发帖数: 125 | 25 Four-manifolds with positive isotropic curvature. R.S. Hamilton.
mathscienet上的链接不行
谢谢啦 |
|
F**S
发帖数: 13 | 26 A question perhaps utterly elementary to riem geometers:
Let M be a compact riemannian manifold and K a geodesic vector field thereon
. How to see that the ricci curvature function Ric(K, K) must be bounded
below everywhere on M by a strictly positive constant? M being compact
should be necessary but does K really have to be geodesic?
Any feedback would be greatly appreciated! |
|
L*m
发帖数: 235 | 27 统计了近十余年来中国大陆高校在四大刊物上的发文，有些是挂名的，但不管如何，还
是都统计了。全名单如下
Annals of Mathematics
A proof of Demailly’s strong openness conjecture
Qi'an Guan（关启安 北京大学） Xiangyu Zhou（周向宇 中科院）
A solution of an L2 extension problem with an optimal estimate and
applications
Qi'an Guan（关启安 北京大学） Xiangyu Zhou（周向宇 中科院）
Construction of Cauchy data of vacuum Einstein field equations evolving to
black holes
Junbin Li（黎俊彬 中山大学） Pin Yu（于品 清华大学）
Special test configuration and K-stability of Fano varieties
Chi Li(李驰 普林斯顿大学 现stony broo... 阅读全帖 |
|
L*******t
发帖数: 2385 | 28 Hi
你可能还停留在heat kernel expansion的层面上。
我说的是把金融资产看成是gauge，通过引入几何结构，在资产空间上可以证明无套利
等价于curvature=0.
是不是你误会了？ |
|
x********i
发帖数: 905 | 29 2016 Breakthrough Prize in Mathematics
The Breakthrough Prize in Mathematics honors the world’s best
mathematicians who have contributed to major advances in the field.
Ian Agol, University of California at Berkeley and Institute for Advanced
Study: for spectacular contributions to low dimensional topology and
geometric group theory, including work on the solutions of the tameness,
virtual Haken and virtual fibering conjectures.
2016 New Horizons in Mathematics Prize
The New Horizons in Mathemat... 阅读全帖 |
|
x********i
发帖数: 905 | 30 http://iccm.mcm.ac.cn/dct/page/1
Plenary Lectures
Group 1
Wei Zhang: RTF and L-functions
Kai-Wen Lan: Cohomology of automorphic bundles
Xinyi Yuan: On Faltings heights of CM abelian varieties
Jing Yu: On Linear Independence of Logarithms
Xuhua He: Cocenter of Hecke algebras
Jiu-Kang Yu: A GAGA theorem for p-adic groups
Jianya Liu: Manin's conjecture for a class of singular cubic
hypersurfaces
Lei Fu: Rigidity of $ell$-adic Sheaves
Si Li: Open-closed topologica... 阅读全帖 |
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p*t
发帖数: 1210 | 31 【 以下文字转载自 Mathematics 讨论区,原文如下 】
发信人: pot (1996年+), 信区: Mathematics
标 题: a geometry question
发信站: Unknown Space - 未名空间 (Fri Apr 15 15:16:13 2005) WWW-POST
I have a profile and revolve it 360degrees. What is the the normal curvature
at an arbitrary point P on the surface? The plot is on the link, but cant be
displayed right.thanks. |
|
b***p
发帖数: 1398 | 32 if there is any difference between the bending torque if bending curvature
and radius is same for the cases above?
thanks, |
|
j****x
发帖数: 943 | 33 This is a typical surface tension related problem. Because of the huge
curvature in capillaries, which is inversely proportional to the tube radius
, you could add surfactant on one side, and hopefully, the fluid inside will
move by itself towards the side without surfactant. Nothing else is
required. |
|
V**y
发帖数: 788 | 34 病理诊断 ：
贲门小弯侧：溃疡型低分化腺癌，局部为印戒细胞癌，侵及全层达浆膜外脂肪，侵犯神
经，累及食管下段。
瓶装上下切缘（－）；网膜（－）。“第2，4，5组”示脂肪。
第3组（1／3）；第1组（1／2）淋巴结见转移癌。
第7组（0／1）；8A（0／2）淋巴结未见转移癌。
Pathology diagnosis:
Cardiac stomach,lesser curvature: ulcerative poorly differentiated
adenocarcinoma with focal signet ring cells, invades full thickness of
stomach wall to periseroal adipose tisse, perineural invasion identified,
lower segment of esophagus involved.
Negative resection margins;negative omentum.
"groups #2, 4, 5" show adipose tissue.
Group #3... 阅读全帖 |
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c*w
发帖数: 50 | 35 30 nm liposome? so small! as I remembered one paper mentioned that the
liposome has a minimum size by calculating the curvature, mechanics etc. |
|
S*****n
发帖数: 6055 | 36 radius of curvature effect in metal-support interaction in catalysis |
|
p******s
发帖数: 62 | 37 If universe is flat, what is the age? How is the age related to the
curvature of the universe?
Pure curious. |
|
C**R
发帖数: 1047 | 38 please calculate how strong a B field u need to bend the proton as much as
you need to bend a electron with the same velocity and the same curvature.
then, u will give up considering proton.
the only reason that i can think of is that the coulomb blur effect (also
called space charge effect) is smaller for protons. You don't loose too much
temporal resolution while ur bunch of protons travel a long way. If you are
not doing ultra-fast, space charge effect is ignorable (hopefully).
please read ja |
|
c*****t
发帖数: 198 | 39 【 以下文字转载自 Biology 讨论区 】
发信人: compact (support), 信区: Biology
标 题: Paper help
发信站: BBS 未名空间站 (Sat Aug 21 00:38:52 2010, 美东)
Q Rev Biophys. 2010 Aug 9;:1-75
Rate theories for biologists.
Huan-Xiang Zhou
Q Rev Biophys. 2010 Feb ;43 (1):65-158 20667175
Structures of membrane proteins.
Kutti R Vinothkumar, Richard Henderson
MRC Laboratory of Molecular Biology, Cambridge, UK.
Q Rev Biophys. 2010 May 18;:1-41 20478077
DNA curvature and flexibility in vitro and in vivo.
Justin P Peters, L James Maher |
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c**********9
发帖数: 33 | 40 Theoretical predictions:
curvature, localized magnetic moments, hydrogen doping, etc.
D. Huertas-Hernando, F. Guinea and A. Brataas, Eur. Phys. J. Spec. Top. 148
(2007), p. 177.
C. Ertler, S. Konschuh, M. Gmitra and J. Fabian, Phys. Rev. B 80 (2009), p.
041405(R).
A.H. Castro Neto and F. Guinea, Phys. Rev. Lett. 103 (2009), p. 026804.
D. Huertas-Hernando, F. Guinea and A. Brataas, Phys. Rev. Lett. 103 (2009),
p. 146801.
Other possible reasons: The short spin life is measured by Hanle effect.
Thi... 阅读全帖 |
|
e*******n
发帖数: 4912 | 41 1.在这个系列里我打算写一些我在各种文章和书中看到的八卦
希望能博大家一笑
有一次littlewood问hardy,为什么他每次到一个旅馆就会把镜子用毛巾盖起来?
回答是:因为他长得太丑了
2.Hadamard,Jacques去意大利Bologna开1928年国际数学家大会,期间要坐火车去一个地
方
车厢里有很多人在聊天,他觉得十分累,就出了道困难的数学题,众人思考这道题,
车厢里马上安静下来了,于是Hadamard就可以睡觉了
3.Bourbaki是一个法国数学家的集体代名词
Bourbaki的第一篇文章发表在comptes Rendus(法国科学院的一个杂志)上
在1949年Journal of symbolic logic上的一篇文章
"Foundations of mathematics for the working mathematican"
中,Bourbaki教授的地址是University of Nancago
一个杜撰的地址,分别是Nancy和Chicago(weil在那里)前后组合
1940年,Boas,Ralph(MR的主编)曾经在Encyclopa... 阅读全帖 |
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e***n
发帖数: 10 | 42 ft，读到human一词才知道ponytail是神马
用词也太误导人了，什么fiber bundle,intrinsic curvatures，gravity
强烈怀疑杂志被编辑的女性家属把持了 |
|
z**********g
发帖数: 16 | 43 Discussing The Existence of “repulsion particle” And Its Significance
Zhuang Yiliong
Shanghai Institute of Science and Technology Management
Abstract:This report has advanced a assume about the existence of “
repellention” by a kind of new idea. Beginning with this, I have explained
more successfully some import theory questions in the area of the present
physics, cosmology and philosophy ect. At same time a few of new reasons
have been raised But this is only rough idea of physica... 阅读全帖 |
|
z**********g
发帖数: 16 | 44 Thesis about the relationship between electron charge
value and electron moving velocity
Yilong Zhuang*
Shanghai Institute of Science and Technology Administration
Jiading,Shanghai 201800
Abstract: “The value of charge has no changes”has not been proved,
but is admitted as a truth.Now that the electron mass can been changed with
it’s moving velocity,then electric charges,as the expression of the
substance’s nature,can be changed accordingly.Following this clue,th... 阅读全帖 |
|
L***6
发帖数: 8307 | 45 对啊，普阿她妈妈的逼啊！ 狗日的学过黎曼几何么？ 数学功底就和shi一样，一看丫
的QFT和广义相对论都没学懂，实验物理丫的也不了解，还平坦宇宙你妈的逼啊？ 时空
curvature和黑洞引起的辐射效应都是实打实观测到的，你妈逼就是个神经病民科 |
|
t**********m
发帖数: 205 | 46 LR106
你的名字应该改成 阿Q，或者阿狗。
我本身就是数学出身的，助教进修班专攻黎曼几何。
时空curvature被验证：
1. 太阳或地球（质点）
2. 没有太阳或地球时，时空是平坦的
所以，广义相对论只是在平坦大尺度背景时空下，质点所带来的局部时空弯曲，在一级
近似下，得到验证！（关于这一点，你可能要学两辈子）。目前，你只是寡头后面吃屎
的分。不要回国再骗同胞，否则你死不瞑目。
你觉得霍金因为黑洞辐射效应，获得了诺贝尔奖？这只是你脑子里的浆糊效应。 |
|
l***y
发帖数: 1166 | 47 4) but the two twin universes have different singularities (in other words:
in our twin cosmos there is not the same number of galaxies, and those
which are there do not have the same structure.) There is not thus another
twin UMMO nor another twin EARTH as one could believe. This last conclusion
is not hypothetical and we will give you its justification.
5) the two cosmos " were created " simultaneously but their arrows of time
are not directed in the same direction. That is, it is illogical ... 阅读全帖 |
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j****e
发帖数: 140 | 48 sorry, I just modified the orginal question.
a need something similar to y=f(x), while the curver have some slope, aka,
it's symetric axis will no long be x=c. |
|
l**n
发帖数: 67 | 49
I agree with what you said, but actually i can have several ways to rephrase
my question.
1: suppose there are two bubbles in a big tank filled with water. The big tank
is in a free fall frame(ignore any external gravitional field). Do the two
bubbles attract, repel or they don't move at all. This is just an excercise of
classical newton mechanics.
2: Take water as the vaccum which means vaccum energy is not zero. In this
highly curved space(with constant positive curvature), how do the two bub |
|
l**n
发帖数: 67 | 50
Just ask a question. Suppose vaccum has energy, it also corresponds to
a certain energy density, right? or certain but finite curvature of the
space time. But energy is still conserved and you still didn't give
a way of making YDJ. |
|
