339 reputation
18
bio website
location China
age 25
visits member for 2 years, 4 months
seen Sep 23 at 13:18
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?
Mar
6
asked When is Dirichlet solution from disk to Riemannian manifold Holder continuous near the boundary?
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
18
revised Dirichlet integral of harmonic functions on manifold controlled by radius?
deleted 183 characters in body
Jan
18
asked Dirichlet integral of harmonic functions on manifold controlled by radius?
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
added 2 characters in body
Jan
12
revised Harmonic function defined on a cone
deleted 105 characters in body
Jan
12
revised Harmonic function defined on a cone
added 108 characters in body
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?
added 45 characters in body
Jan
10
revised Dirichlet energy of a harmonic function bounded above by the energy of the boundary function?
added 7 characters in body
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?