bio | website | |
---|---|---|
location | China | |
age | 26 | |
visits | member for | 3 years |
seen | Dec 6 '14 at 4:54 | |
stats | profile views | 840 |
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? |