Timeline for Convex functions in convex sets
Current License: CC BY-SA 4.0
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jul 22, 2023 at 16:39 | comment | added | Stefan Steinerberger | I'd definitely be interested!! | |
| Jul 21, 2023 at 1:58 | comment | added | fedja | @StefanSteinerberger OK, I believe that we (I and Dmitry Ryabogin) can prove it in full generality in 2D as conjectured. For $n>2$ it fails even for some symmetric sets. Let me know if anybody still cares and, if yes, I'll try to post the argument :-) | |
| Jul 17, 2023 at 11:59 | comment | added | fedja | It is true for symmetric domains in 2D. Not sure about the coinciding centers of mass condition yet. | |
| Jun 4, 2023 at 2:15 | comment | added | Lev Borisov | I think that the problem can essentially be reduced to convex polytopes and piecewise linear functions. If there were a counterexample, one should be able to approximate both the function and the region, while keeping the centers of mass equality. | |
| May 28, 2023 at 19:57 | comment | added | Stefan Steinerberger | The unit ball is naturally special and stronger things can be said: there, the inequality is actually true for all subharmonic functions with constant 1 (this follows relatively quickly from the maximum principle and the mean value theorem for harmonic functions). As for the ellipse: I don't think this is likely to be a counterexample, the level sets {|x| = c} get shorter when c gets large while the boundary measure stays roughly constant. | |
| May 28, 2023 at 16:39 | history | answered | Christophe Leuridan | CC BY-SA 4.0 |