18,986 reputation
561147
bio website math.psu.edu/petrunin
location Penn State
age 47
visits member for 5 years, 10 months
seen 23 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.


2d
awarded  reference-request
2d
awarded  Nice Answer
2d
comment Set of regular points in an Alexandrov space with curvature bounded below
@sva, yes, semiconcave functions on Alexandrov space have well defined Hessian almost everywhere (4.4 in math.psu.edu/petrunin/papers/alexandrov/Cstructure.pdf).
2d
answered Set of regular points in an Alexandrov space with curvature bounded below
Aug
29
answered Advanced Differential Geometry Textbook
Aug
28
answered Basic question about discrete minimal surfaces
Aug
28
comment A compact Alexandrov space with curvature bounded below has curvature bouneded above?
First read the definitions :) Then take the surface of convex polytope; it has curvature bounded below, but no upper curvature bound.
Aug
27
revised If all ball around fised basepoints are isometric, are the spaces as well (length spaces)?
deleted 593 characters in body
Aug
25
answered If all ball around fised basepoints are isometric, are the spaces as well (length spaces)?
Aug
25
comment Matrix equation $XAXBXC=I$
This idea appears in paper of Gerstenhaber and Rothaus. The degree of the map was calculated by Hopf in "Ueber den Rang ..."
Aug
25
awarded  Nice Question
Aug
25
comment Are ultralimits the Gromov-Hausdorff limits of a subsequence?
Yes it is true and follow directly from the definition. However it is not true that the sequence can be found in the ultrafilter, see mathoverflow.net/questions/111842
Aug
25
comment Square of the distance function on a Riemannian manifold
All the coefficients of degree 3 vanish.
Aug
24
awarded  Great Question
Aug
24
comment Is a cocompact CAT(0) periodic?
Take countably many copies of an isosceles triangle and glue them together in a chain along the equal sides. By Reshetnyak's theorem, you get a $\mathrm{CAT}[0]$-space, say $X$. $X$ admits a cocompact action of $\mathbb{Z}$, but all cocompact actions have a fixed point. Therefore they do not come from a covering map $X\to C$, so it is not periodic.
Aug
18
revised Closed geodesic loops around points in compact manifolds
+ref
Aug
16
comment set of centers of sphere inscribed in tetrahedron
@JosephO'Rourke, ignore it, it was a comment to the old version of the question where $D$ is arbitrary.
Aug
15
comment set of centers of sphere inscribed in tetrahedron
The boundary of the set is formed by incenters of tetrahedra with $D$ at infinity. Do not expect it to be particular nice surface.
Aug
9
comment Harmonic map heat flow in positive curvature
If you just need to smooth, you can apply a convolution with a reasonable kernel (cheap and easy).
Aug
8
accepted Terminology for polygons