Remarks on $L^{p}$-vanishing results in geometric analysis

Details Remarks on $L^{p}$-vanishing results in geometric analysis Remarks on $L^{p}$-vanishing results in geometric analysis

2010-11-24

arxiv.org/abs/1011.5413v2

Mathematics

Differential Geometry

18 pages. Some oversights corrected. Accepted for publication in International Journal of Mathematics

Scientific paper

We survey some $L^{p}$-vanishing results for solutions of Bochner or Simons type equations with refined Kato inequalities, under spectral assumptions on the relevant Schr\"{o}dinger operators. New aspects are included in the picture. In particular, an abstract version of a structure theorem for stable minimal hypersurfaces of finite total curvature is observed. Further geometric applications are discussed.

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