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Jan
26
reviewed Approve Elementary divisibility problem.
Jan
26
answered Prove that the following statements are equivalent
Jan
26
answered Prove with use of derivative
Jan
16
comment Umbilics on the ellipsoid
Yes it is right
Jan
16
comment Umbilics on the ellipsoid
I did not calculate wrt your posting but f is given by root so that for f_xx we must differentiate twice (Still it may be long computation) but it may be easy Try it
Jan
16
comment Umbilics on the ellipsoid
Yes it is correct
Jan
16
comment Umbilics on the ellipsoid
Umbilics implies that square of mean curvature is equal to K
Jan
16
comment Umbilics on the ellipsoid
We must find Gaussian curvature K
Jan
14
accepted To construct a continuous map on compact metric spaces (cf. Gromov-Hausdorff Limit)
Jan
14
comment To construct a continuous map on compact metric spaces (cf. Gromov-Hausdorff Limit)
Thank you for your answer.
Jan
13
comment To construct a continuous map on compact metric spaces (cf. Gromov-Hausdorff Limit)
And to first question, $f : B_r(0) \rightarrow Z$ is an isometry for a fixed $r$
Jan
13
comment To construct a continuous map on compact metric spaces (cf. Gromov-Hausdorff Limit)
Yes as far as I know. And if there exists such $Z$, then we say $d_{GH}(X,Y)<\epsilon $. If $\epsilon$ is large, for instance it is a large constant depending on ${\rm diam}\ X,\ {\rm diam}\ Y$, we can build such $Z$
Jan
13
revised To construct a continuous map on compact metric spaces (cf. Gromov-Hausdorff Limit)
deleted 6 characters in body
Jan
13
revised To construct a continuous map on compact metric spaces (cf. Gromov-Hausdorff Limit)
deleted 6 characters in body
Jan
13
comment To construct a continuous map on compact metric spaces (cf. Gromov-Hausdorff Limit)
I wanted to write simpler but it is difficult. So I rewrite
Jan
13
revised To construct a continuous map on compact metric spaces (cf. Gromov-Hausdorff Limit)
added 775 characters in body; edited title
Jan
12
revised To construct a continuous map on compact metric spaces (cf. Gromov-Hausdorff Limit)
deleted 85 characters in body
Jan
12
comment To construct a continuous map on compact metric spaces (cf. Gromov-Hausdorff Limit)
I see. I want to emphasize that there exist several points $x'$ I will fix it.
Jan
12
comment To construct a continuous map on compact metric spaces (cf. Gromov-Hausdorff Limit)
And since $f$ is isometric then $f(X)$ is still convex in arbitrary metric space : In any two points $y_i$ in $f(X)$ there exists a shortest path $c$ between $x_i:=f^{-1}(y_i)$ So $$l(f\circ c)=l(c)=d_0(x_1,x_2)=d(y_1,y_2) $$
Jan
12
comment Limit of Riemannian manifolds is not Riemannian
Let $c(t)$ be a path between $c(0)=a$ and $c(1)=b$ Define a length $l(c):=\inf_P \sum_{i=1}^n d(c(t_i),c(t_{i+1}) )$ where $P$ is a partition If $l(c)=d(a,b)$, then $c$ is shortest. And I can not understand "cannot associate"