bio  website  math.psu.edu/petrunin 

location  Penn State  
age  47  
visits  member for  5 years, 10 months 
seen  23 mins ago  
stats  profile views  11,734 
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.
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awarded  referencerequest 
2d

awarded  Nice Answer 
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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). 
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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 GromovHausdorff 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 