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location China
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visits member for 2 years, 10 months
seen Dec 6 '14 at 4:54
mathboy

Sep
24
awarded  Autobiographer
May
17
comment both convex and superharmonic function on manifold concave?
By mollification, we can get a sequence of smooth functions converging to f. But I don't know the convexity and Laplacian of these functions
May
17
asked both convex and superharmonic function on manifold concave?
Feb
18
comment harmonic maps from cone to $S^2$ locally lipschitz?
:Just as you have said before. Take the cone as a sector with total angel $\alpha<2\pi$. Then $\phi^{-1}$ is $z\mapsto z^{\pi/\alpha}$. It seems to me this map is also locally Lipshcitz(hence every harmonic map is locally lipschitz).
Feb
17
asked harmonic maps from cone to $S^2$ locally lipschitz?
Jan
16
comment Dirichlet energy of a harmonic function bounded above by the energy of the boundary function?
@ConnorMooney:I wonder whether we can get a similar estimate in two-dimensional manifolds. At least I think the dirichlet integral can be bounded above by a number w.r.t the boundary value f..
Jan
12
comment Harmonic function defined on a cone
@Andrew:For a disk, your answer is OK. But for a cone(It's not a $C^1$ manifold), it's not so obvious.
Jan
12
revised Harmonic function defined on a cone
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Jan
12
revised Harmonic function defined on a cone
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Jan
12
revised Harmonic function defined on a cone
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Jan
12
asked Harmonic function defined on a cone
Jan
12
comment Dirichlet energy of a harmonic function bounded above by the energy of the boundary function?
@Alexandre Eremenko:If we consider harmonic functions defined on a two-dimension cone. Take$$z=x^2+y^2,x^2+y^2\leq1$$ for example. What's the regularity of the boundary value f that can make sure there is a harmonic function u on the cone? And what is the regularity of u, does u satisfy the Green's formula and the inequality I asked?
Jan
11
comment Dirichlet energy of a harmonic function bounded above by the energy of the boundary function?
Monney:for general domain in $R^n$(or $R^2$), is there a similar inequality?
Jan
10
revised Dirichlet energy of a harmonic function bounded above by the energy of the boundary function?
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Jan
10
revised Dirichlet energy of a harmonic function bounded above by the energy of the boundary function?
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Jan
10
asked Dirichlet energy of a harmonic function bounded above by the energy of the boundary function?
Nov
6
comment When does heat kernel have both Gaussian upper and lower bounds?
:And for manifold with Ricci bounded from below, we can get neither a scale invariant doubling nor a scale invariant Poincare?
Nov
6
comment When does heat kernel have both Gaussian upper and lower bounds?
:You mean scale invariant doubling plus scale invariant Poincare equivalent to Gaussian two-sided bounds?
Oct
9
awarded  Caucus
Oct
8
asked How to construct a harmonic function with non-zero gradient on manifold with two nonparabolic ends?