A Poincaré Formula for Differential Forms and Applications

• Published in: Symmetry, Integrability and Geometry: Methods and Applications
• Date: 2023
• Main Authors: Ginoux, Nicolas, Habib, Georges, Raulot, Simon
• Format: Article
• Language: English
• Published: Інститут математики НАН України 2023
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/212043
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: A Poincaré Formula for Differential Forms and Applications. Nicolas Ginoux, Georges Habib and Simon Raulot. SIGMA 19 (2023), 088, 17 pages

We prove a new general Poincaré-type inequality for differential forms on compact Riemannian manifolds with nonempty boundary. When the boundary is isometrically immersed in Euclidean space, we derive a new inequality involving mean and scalar curvatures of the boundary only and characterize its lim...