Timeline for Curve integral of exponent of superharmonic function.
Current License: CC BY-SA 2.5
16 events
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| Apr 13, 2017 at 12:58 | history | edited | CommunityBot |
replaced http://mathoverflow.net/ with https://mathoverflow.net/
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| Jun 25, 2013 at 15:31 | vote | accept | Anton Petrunin | ||
| May 30, 2011 at 23:44 | answer | added | fedja | timeline score: 5 | |
| Apr 14, 2011 at 15:53 | answer | added | Igor Belegradek | timeline score: 3 | |
| Apr 5, 2011 at 4:22 | history | bounty ended | Anton Petrunin | ||
| Apr 3, 2011 at 17:35 | history | edited | Anton Petrunin |
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| Mar 31, 2011 at 7:31 | comment | added | Syang Chen | Alternatively, is it possible to show that(at least for those $\phi$ that you are interested in) $\int_{D} e^{\phi}dx<\infty$? If it is the case, then almost every radius could serve your purpose. As far as I know, $L^p$ integrability of $(\phi)_{+}$ always holds for some $p>0$. | |
| Mar 31, 2011 at 7:30 | comment | added | Syang Chen | @Anton, here is another "greedy curve" which will touch the boundary in finite time: let $|\gamma(r)|=r$ such that $\phi (\gamma(r))=$ min$_{|z|=r} \phi (z)$, where $ 0 \leq r < 1 $. But I am not sure if such $\gamma$ exists, and more importantly, if it has finite length. | |
| Mar 29, 2011 at 23:35 | comment | added | Anton Petrunin | @Xianghong, this way you at least decrease $\phi$ along $\gamma$, but you might get a curve of infinite length (I do not see why not). | |
| Mar 29, 2011 at 21:14 | comment | added | Syang Chen | How about using "greedy algorithm" to choose γ? That is, let γ(0)=0,dγ=−∇ϕ(γ) so that $e^ϕ$ is minimized in each infinitesimal step. Can superharmonicity of ϕ guarantee that γ will touch the boundary eventually, to begin with? | |
| Mar 29, 2011 at 3:23 | history | bounty started | Anton Petrunin | ||
| Mar 27, 2011 at 23:32 | history | edited | Anton Petrunin | CC BY-SA 2.5 |
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| Mar 17, 2011 at 21:57 | history | edited | Anton Petrunin | CC BY-SA 2.5 |
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| Mar 17, 2011 at 20:10 | history | edited | Anton Petrunin | CC BY-SA 2.5 |
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| Mar 17, 2011 at 19:24 | history | edited | Anton Petrunin | CC BY-SA 2.5 |
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| Mar 17, 2011 at 16:09 | history | asked | Anton Petrunin | CC BY-SA 2.5 |