M****i
发帖数: 58 | 1 Let M be a Riemannian manifold, x and y are two pints in M. Assume that x is
not in the cut locus of y, then whether there exist a neighborhood U of x
and a neighborhood V of y such that for every point u in U and for every
point v in V we have that u is not in the cut locus of v? |
l********e
发帖数: 3632 | 2 yes, since it's closed set |
M****i
发帖数: 58 | 3 Thank you very much for your answer!
Is the closed set in your post is
{(x,y)\in M^2: x is in the cut locus of y}?
Could you please give a short proof for this? Or some references? Many thanks!
【在 l********e 的大作中提到】
: yes, since it's closed set
|
l********e
发帖数: 3632 | 4 cut locus在tangent space中是同胚于球面所以closed，exp的像也是closed的。
可以看Cheeger-Ebin
中文看伍鸿禧的黎曼几何初步
thanks!
【在 M****i 的大作中提到】
: Thank you very much for your answer!
: Is the closed set in your post is
: {(x,y)\in M^2: x is in the cut locus of y}?
: Could you please give a short proof for this? Or some references? Many thanks!
|
M****i
发帖数: 58 | 5 Ok, thanks!
【在 l********e 的大作中提到】
: cut locus在tangent space中是同胚于球面所以closed，exp的像也是closed的。
: 可以看Cheeger-Ebin
: 中文看伍鸿禧的黎曼几何初步
:
: thanks!
|
