List questions from harmonic-functions

Published on 27 Sep 2013 - 3:37

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How to prove a harmonic function is a polynomial?

Published on 29 Sep 2013 - 16:22

392

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How to prove a harmonic function to be smooth?

Published on 29 Sep 2013 - 16:46

178

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a version of the comparison lemma (harmonic functions)

Published on 30 Sep 2013 - 2:05

114

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Form of a harmonic function

Published on 30 Sep 2013 - 6:17

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Show that $\widetilde{u} \in PSH(\Omega)$

Published on 27 Mar 2026 - 14:45

280

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Show that a $C^2$-function $u$ is plurisubharmonic if and only if the Hessian matrix $H_u(z)(\omega, \omega)>0$

Published on 27 Mar 2026 - 14:52

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A family of curves orthogonal to another family. How to graph this?

Published on 06 Oct 2013 - 13:10

196

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Prove that $u \circ f $ is plurisubharmonic on $\Omega_1$

Published on 27 Mar 2026 - 14:54

125

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can the gradient of a harmonic function =0 at some interior point of a manifolds with two ends?

Published on 08 Oct 2013 - 13:18

148

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Hausdorff dimension of support of harmonic measure in complex plane

Published on 08 Oct 2013 - 17:33

1.1k

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Harmonic function (PDE) - Orthogonal matrix

Published on 09 Oct 2013 - 12:27

69

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For which real constants $k$ is the function $u$ harmonic?

Published on 31 Mar 2026 - 21:05

2.5k

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Harmonic function vanishes with its normal derivative on a part of boundary; can Green's formula be applied to broken boundary?

Published on 12 Oct 2013 - 17:29

211

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How to construct a minimizing sequence?

Published on 26 Mar 2026 - 18:49

List Question

subharmonic function and support functions

How to prove a harmonic function is a polynomial?

How to prove a harmonic function to be smooth?

a version of the comparison lemma (harmonic functions)

Form of a harmonic function

Show that $\widetilde{u} \in PSH(\Omega)$

Show that a $C^2$-function $u$ is plurisubharmonic if and only if the Hessian matrix $H_u(z)(\omega, \omega)>0$

A family of curves orthogonal to another family. How to graph this?

Prove that $u \circ f $ is plurisubharmonic on $\Omega_1$

can the gradient of a harmonic function =0 at some interior point of a manifolds with two ends?

Hausdorff dimension of support of harmonic measure in complex plane

Harmonic function (PDE) - Orthogonal matrix

For which real constants $k$ is the function $u$ harmonic?

Harmonic function vanishes with its normal derivative on a part of boundary; can Green's formula be applied to broken boundary?

How to construct a minimizing sequence?

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