ScholarWorks@숙명여자대학교

초록

Let Σ be a free boundary biharmonic hypersurface in the Euclidean unit ball Bm+1. Denote by H the mean curvature function on Σ. We prove that Σ satisfies a sharp linear isoperimetric inequality mVol(Σ)≤Vol(∂Σ), where equality holds if and only if Σ is a free boundary minimal hypersurface. Moreover, we prove that Σ is minimal if either H is constant along the boundary or H∂H∂ν is nonpositive along the boundary, where ν denotes the outward unit conormal vector. These results can be thought of as a partial affirmative answer to Chen’s conjecture.

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