Abstract
We study the stability of capillary hypersurfaces in a unit Euclidean ball. It is proved that if the center of mass of the domain enclosed by the immersed capillary hypersurface and the wetted part of the sphere is located at the origin, then the hypersurface is unstable. An immediate result is that all known examples except the totally geodesic ones and spherical caps are unstable. We also conjecture a precise delineation of the stable capillary hypersurfaces in unit Euclidean balls.
| Original language | English |
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| Pages (from-to) | 131-146 |
| Number of pages | 16 |
| Journal | Pacific Journal of Mathematics |
| Volume | 297 |
| Issue number | 1 |
| DOIs | |
| Publication status | Published - 2018 |