Convexity of λ-hypersurfaces
classification
🧮 math.DG
math.AP
keywords
lambdaconvexhypersurfacescloseddimensionalmeanconvexitycorollary
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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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