17,683 reputation
357142
bio website math.psu.edu/petrunin
location Penn State
age 46
visits member for 5 years, 1 month
seen 3 hours ago

A description from 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.


11h
revised Is the “Napkin conjecture” open? (origami)
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2d
revised Nonperiodic points of piecewise-linear homeomorphisms
added 303 characters in body
Dec
19
revised Diameter of m-fold cover
deleted 116 characters in body
Dec
19
comment Is the blowing up the rectifiable set cone?
Well first formulate the question correctly :)
Dec
19
awarded  Nice Answer
Dec
18
comment Is the blowing up the rectifiable set cone?
The question is not formulated well, but it seems that the answer is NO for any reformulation.
Dec
18
comment Nonperiodic points of piecewise-linear homeomorphisms
@JamesPropp: the answer is updated.
Dec
18
revised Nonperiodic points of piecewise-linear homeomorphisms
added 291 characters in body
Dec
18
comment Nonperiodic points of piecewise-linear homeomorphisms
@JamesPropp, I do not see how bounty may help here, you should tell what is not clear --- then I can help.
Dec
16
comment Nonperiodic points of piecewise-linear homeomorphisms
@JamesPropp: if a point $x\in \triangle'$ is close to the base of $\triangle'$ then $T^n$ moves it slowly. So number of iterations of $T^n$ keeps the point in $\triangle'$ and the orbit $x_k=T^{n\cdot k}(x)$ is very predictable.
Dec
13
comment Nonperiodic points of piecewise-linear homeomorphisms
P.S. Nice question, can you tell why did you need it?
Dec
13
comment Nonperiodic points of piecewise-linear homeomorphisms
@JamesPropp: Given a poisitive integer $K$ you can find an open rectangle $\square$ near the base of $\triangle'$ such that $\square\cap E_k=\varnothing$ for any $k<K$.
Dec
12
revised Nonperiodic points of piecewise-linear homeomorphisms
added 169 characters in body
Dec
12
answered Nonperiodic points of piecewise-linear homeomorphisms
Dec
7
comment What introductory book on Graph Theory would you recommend?
I used this book to teach a course this semester, the students liked it and it is a very good book indeed. [The book includes number of quasiindependent topics; each introduce a brach of graph theory and avoids tecchnicalities. I would include in addition basic results in algebraic graph theory, say Kirchhoff's theorem, I would expand the chapter on Algorithms, but the book is VERY GOOD anyway.]
Dec
2
comment Besicovitch's covering theorem for ellipsoids and shadows
Check this answer, it seems to be related mathoverflow.net/a/127928
Nov
27
revised another question about connected open sets in $R^2$
added 9 characters in body
Nov
27
answered another question about connected open sets in $R^2$
Nov
24
comment Normal Variation on Manifolds
OK, you want to bound the Lipschitz constant of the Gauss map in terms of normal curvatures. This is a question in linear algebra. Set $q(x,y,z,w)=\langle s(x,y),s(z,w)\rangle$ then you get all the values $q(x,x,x,x)$ and you need to estimate $\sum q(u,e_i,u,e_i)$, but I am too lazy.
Nov
24
comment Normal Variation on Manifolds
@user62013 Well, the "principle curvatures" are not defined if codimension $>1$.