Timeline for Harmonic functions on the plane
Current License: CC BY-SA 3.0
4 events
| when toggle format | what | by | license | comment | |
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| Oct 2, 2011 at 8:43 | comment | added | Alexander Isaev | In fact, I think I know how to adapt your proof to this more general situation. One has to consider the region where $-kA<v<nA$ for suitable $k$, $n$. | |
| Oct 2, 2011 at 6:13 | comment | added | Alexander Isaev | Thank you very much for your solution. Your argument proves that there exists no non-constant harmonic map from the plane into the domain in the plane lying above the cubic parabola $y>x^3$. Consider now the region defined as follows: $y>tx^3$ for $x\ge 0$ and $y>sx^3$ for $x<0$, where $s,t>0$. If one applies your argument to this more general domain, it seems that the answer depends on $s$ and $t$. However, I believe that there is no non-constant map into this domain for any $s$ and $t$. Can your proof be adopted to the case of general $s$ and $t$? Alex Isaev. | |
| Oct 2, 2011 at 6:09 | vote | accept | Alexander Isaev | ||
| Oct 1, 2011 at 16:37 | history | answered | fedja | CC BY-SA 3.0 |