Entropies and CMC hypersurfaces

Université François Rabelais

Let MM be a complete, noncompact constant mean curvature hypersurface of finite index in Rn+1\mathbb{R}^{n+1} . We show that if either MM has zero volume entropy, or zero total curvature entropy and n5n \leq 5, or has bounded curvature and is properly embedded, then MM is minimal. We obtain similar results in more general ambient manifolds. Moreover the article contains some results of independent interest, about the volume entropy and the bottom of the essential spectrum.

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This activity is supported by the research projects EUR2024.153556, PID2023-150727NB-I00, , PID2023-151060NB-I00, PID2022-142559NB-I00, CNS2022-135390 CONSOLIDACION2022, PID2020-118137GB-I00, PID2020-117868GB-I00, PID2020-116126GB-I00.