Total Mean Curvature and First Dirac Eigenvalue

• Published in: Symmetry, Integrability and Geometry: Methods and Applications
• Date: 2023
• ISSN: 1815-0659
• Main Author: Raulot, Simon
• Format: Article
• Language: English
• Published: Інститут математики НАН України 2023
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/211914
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: Total Mean Curvature and First Dirac Eigenvalue. Simon Raulot. SIGMA 19 (2023), 029, 14 pages

In this note, we prove an optimal upper bound for the first Dirac eigenvalue of some hypersurfaces in the Euclidean space by combining a positive mass theorem and the construction of quasi-spherical metrics. As a direct consequence of this estimate, we obtain an asymptotic expansion for the first ei...