Bulletin of the Korean Mathematical Society (대한수학회보)

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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)
  • Received : 2021.06.01
  • Accepted : 2021.11.08
  • Published : 2022.05.31
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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.

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Acknowledgement

The author would like to express his thanks to Prof. Nguyen Thac Dung for drawing his attention to this topic and useful discussion during the preparation of this work. The author was partially supported by Vingroup Innovation Foundation VINIF under grant number VINIF.2019. ThS.18.

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