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359144
bio website math.psu.edu/petrunin
location Penn State
age 47
visits member for 5 years, 6 months
seen 7 hours 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.


1h
awarded  Nice Answer
2d
comment Does the Riemann-Christoffel 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 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 $f$.