bio  website  math.psu.edu/petrunin 

location  Penn State  
age  47  
visits  member for  5 years, 6 months 
seen  7 hours ago  
stats  profile views  11,360 
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.
1h

awarded  Nice Answer 
2d

comment 
Does the RiemannChristoffel curvature determine the connection?
For the connections with torsion the question gets easier. 
2d

comment 
Perturb a given smooth function to a Morse function relative to fixed level sets, which are already fine
@Francis: Now it is corrected. 
2d

revised 
Perturb a given smooth function to a Morse function relative to fixed level sets, which are already fine
added 18 characters in body 
May 21 
revised 
Perturb a given smooth function to a Morse function relative to fixed level sets, which are already fine
added 68 characters in body 
May 21 
answered  Perturb a given smooth function to a Morse function relative to fixed level sets, which are already fine 
May 15 
comment 
Fundamental groups of stably parallelizable manifolds
@QiaochuYuan, For closed you can take the doubling and realize it as a hypesurface in $\mathbb R^{n+1}$, the result is stably parallelizable. 
May 6 
comment 
Two surfaces with zero gaussian curvature
So, do you expect that $f$ and $g$ have form $a(t)+b\cdot s$? 
Apr 28 
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 HopfRinow theorem). You need to show that finite dimensional Alexandrov spaces are locally compact. The later is proved already in BuragoGromovPerelman. 
Apr 12 
asked  biLipschitz 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 $f$. 