Convexity of $λ$-hypersurfaces

Published 12 Apr 2021 in math.DG and math.AP | (2104.05464v2)

Abstract: We prove that any $n$-dimensional closed mean convex $\lambda$-hypersurface is convex if $\lambda\le 0.$ This generalizes Guang's work on $2$-dimensional strictly mean convex $\lambda$-hypersurfaces. As a corollary, we obtain a gap theorem for closed $\lambda$-hypersurfaces with $\lambda\le 0.$

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Tang-Kai Lee

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