A Reilly inequality for some natural elliptic operators on hypersurfaces

✍ Scribed by Jean-François Grosjean

• Book ID: 104358089
• Publisher: Elsevier Science
• Year: 2000
• Tongue: English
• Weight: 71 KB
• Volume: 13
• Category: Article
• ISSN: 0926-2245
• DOI: 10.1016/s0926-2245(00)00024-3

✦ Synopsis

Let M n be a compact hypersurface of a real space form and L r the linearized operator of the first variation of the (r + 1)th mean curvature, r ∈ {0, . . . , n}. In this paper, we obtain an optimal upper bound for the first eigenvalue of those operators L r , in terms of the r th mean curvatures of M.