18,466 reputation
359143
bio website math.psu.edu/petrunin
location Penn State
age 46
visits member for 5 years, 5 months
seen 3 mins ago

A description by my son:

Mein Vater hat keine Haare aber er hat einen schwarzen Bart. Er hat grüne Augen so wie ich. Er benutzt seine Brille sehr selten. Sein Name ist Tosha. Er mag Musik spielen aber ist ganz schlecht dabei und ist 44 Jahre alt.


1m
revised Are there smooth bodies of constant width?
added 4 characters in body
Apr
12
comment Gradient estimate of convex functions
$g$ is piecewise linear (not piecewise constant).
Apr
12
comment Gradient estimate of convex functions
You can find a counterexample for $d=1$ among functions which are linear on each interval $[n,n+1]$.
Apr
12
comment Existence of shortest paths in complete Alexandrov spaces
Well, this is true for any locally compact lenght metric space (see Hopf--Rinow theorem). You need to show that finite dimensional Alexandrov spaces are locally compact. The later is proved already in Burago-Gromov-Perelman.
Apr
12
asked bi-Lipschitz gluing
Apr
6
comment Terminology for metrics?
In this case, you can assume that $C=1$. In this case it is called $E$-isometry. Usually it is assumed that $E$ is small, but one does not have to do that. The identity map $(X,d)\to (X,\delta)$ is also called $E$-Hausdorff approximation. Hope it helps.
Apr
5
comment Smoothing operator raising the smoothness exactly by one
@IgorBelegradek, I think you know what I mean, do not you?
Apr
5
comment Smoothing operator raising the smoothness exactly by one
@IgorBelegradek corrected.
Apr
5
revised Smoothing operator raising the smoothness exactly by one
added 89 characters in body
Apr
4
answered Smoothing operator raising the smoothness exactly by one
Apr
4
comment Smoothing operator raising the smoothness exactly by one
@IgorBelegradek, obviously I meant $$\varepsilon\cdot\int\limits_0^x(f(t)-\bar f)\cdot dt.$$
Apr
4
comment Smoothing operator raising the smoothness exactly by one
For $M=\mathbb S^1$ one can take $C^\infty$-smoothing and add $\varepsilon\cdot\int (f(x)-\bar f)\cdot dx$, where $\bar f$ is the average value of $f$.
Apr
3
comment convex decompositions of the sphere
Yes, and hopefully the formula is correct.
Apr
3
answered convex decompositions of the sphere
Mar
31
comment Generalize Gauss-Bonnet Formula to non-simple closed curves
@AlexDegtyarev, you are right, "it is freshmen differential geometry", but you wrong about right hand side.
Mar
28
comment Lower boundedness of the Ricci curvature
@AlexM. it simply impossible to give an answer here, one has to write 20 pages or so and yes Gromov's "Sign and geometric meaning of curvature" is a good sours.
Mar
27
comment Lower boundedness of the Ricci curvature
Way too vague for me.
Mar
24
answered distributional Hessian for semiconvex functions on non-smooth manifolds
Mar
14
comment Are there CAT(-1) spaces which are not trees whose Gromov boundary is disconnected?
word hyperbolic groups are not exactly CAT(-1). (But there are many examples.)
Mar
14
answered Are there CAT(-1) spaces which are not trees whose Gromov boundary is disconnected?