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arXiv · 1807.06849

Vanishing theorems for the cohomology groups of free boundary hypersurfaces

Marcos P. Cavalcante·Abraão Mendes·Feliciano Vitório
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Abstract

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

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Marcos P. Cavalcante, Abraão Mendes, Feliciano Vitório. 2018-11-22. Vanishing theorems for the cohomology groups of free boundary hypersurfaces. https://arxiv.org/abs/1807.06849

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