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Nov
26
comment Divergence free vector field on compact surface
Tes m'y question can be reformulate as follow: what is the asymptotic behaviour of harmonic one form when the conformal class degenerate?
Nov
25
answered How to prove the Hölder continuity of a function $u$ by evaluating $\int_{B_{\rho}(x_0)}\frac{|Du(x)|^{2}}{|x-x_0|^{n-2}} dx$?
Nov
24
asked Divergence free vector field on compact surface
Nov
21
answered Compact surface with arbitrarily large eigenvalue
Oct
23
revised harmonic extension of a curve by different parametrization
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Oct
22
revised harmonic extension of a curve by different parametrization
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Oct
19
comment Elliptic regularity for two dimensional domains
Yes it is. If u=ln(ln(r)), then \nabla u \in L^2 but conclusion fails
Oct
19
answered Elliptic regularity for two dimensional domains
Oct
18
awarded  Nice Question
Oct
18
comment Regularity up to the boundary for the Poisson problem
you can llok to Gilbard Trudinger or the courant lecture notes by Han Lin
Oct
18
comment Gauss curvature flow
Is that clear, that the condition $\langle x, \nu \rangle=K$ is preserved? Else it looks good.
Oct
18
comment harmonic extension of a curve by different parametrization
Thanks for the Answer. The first point was indeed "easy". In fact I know quite well the solution of Douglas-Rado (through Struwe's book). lik in lawson, he minimise the energy among conformal parametrisation. But since my goal is 3)(1) and 2) are a try to make more explicit), it can't be adapted here. If we consider $h:z\mapsto z+ z^2/4$ , $\vert h(\mathbb{D})\vert=9/8$, but $\vert h'(0)\vert=1$ and any conformal reparametrization(using mobius group) will be below $9/8$.
Oct
17
revised harmonic extension of a curve by different parametrization
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Oct
17
revised harmonic extension of a curve by different parametrization
edited tags
Oct
16
revised harmonic extension of a curve by different parametrization
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Oct
16
revised harmonic extension of a curve by different parametrization
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Oct
16
asked harmonic extension of a curve by different parametrization
Sep
16
answered Equivalence of Harmonic Maps and Conformal Maps on Genus-0 closed surfaces
Jun
25
comment Decomposition of a closed surface
yes I mean homotopy. have you a reference for the pants decomposition? because I need minimizing representant without intersection... who is Shepard?Thx
Jun
24
comment Decomposition of a closed surface
Thanks for the answer. Can you give me more references. Notably,about the theorem you invoke. it is not totally clear to me since an homology class is like a open cylinder, and without the negative curvature assumption, perhaps the minimum is not achieved? And I didn't also find a Shepard at UCB... Thanks again for your help!!