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http://dx.doi.org/10.4134/BKMS.b210426

FINITENESS AND VANISHING RESULTS ON HYPERSURFACES WITH FINITE INDEX IN ℝn+1: A REVISION  

Van Duc, Nguyen (Department of Mathematics University of Science Vietnam National University)
Publication Information
Bulletin of the Korean Mathematical Society / v.59, no.3, 2022 , pp. 709-723 More about this Journal
Abstract
In this note, we revise some vanishing and finiteness results on hypersurfaces with finite index in ℝn+1. When the hypersurface is stable minimal, we show that there is no nontrivial L2p harmonic 1-form for some p. The our range of p is better than those in [7]. With the same range of p, we also give finiteness results on minimal hypersurfaces with finite index.
Keywords
Finite index; finiteness result; harmonic forms; minimal hypersurfaces; rigidity theorem;
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