Vanishing theorems for the cohomology groups of free boundary hypersurfaces

2018/07/18 by Marcos P. Cavalcante, Cavalcante, Marcos P., Abraão Mendes +3
Mathematics · #Differential Geometry (math.DG) #FOS: Mathematics #math.DG

paper · pdf · doi:10.48550/arxiv.1807.06849

Version with improved constants. The authors thank Ezequiel Barbosa for valuable comments on this paper

arxiv created 2018/11/22 · arxiv updated 2018/11/26

Abstract

In this paper, we prove that there exists a universal constant C, depending only on positive integers n≥ 3 and p≤ n-1, such that if Mⁿ is a compact free boundary submanifold of dimension n immersed in the Euclidean unit ball \mathbbB^n+k whose size of the traceless second fundamental form is less than C, then the pth cohomology group of Mⁿ vanishes. Also, employing a different technique, we obtain a rigidity result for compact free boundary surfaces minimally immersed in the unit ball \mathbbB^2+k.

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