Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Remarks on $L^{p}$-vanishing results in geometric analysis   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.

15
The categories of this paper are: nucl-ex
23
The categories of this paper are: solv-int
27
The categories of this paper are: comp-gas
3
The categories of this paper are: physics
32
The categories of this paper are: atom-ph
12
The categories of this paper are: nucl-th
13
The categories of this paper are: quant-ph
36
The categories of this paper are: cmp-lg
19
The categories of this paper are: eess
29
The categories of this paper are: funct-an
1
The categories of this paper are: cs
22
The categories of this paper are: chao-dyn
7
The categories of this paper are: hep-th
8
The categories of this paper are: hep-ex
6
The categories of this paper are: astro-ph
11
The categories of this paper are: hep-lat