Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Absence of bubbling phenomena for non convex anisotropic nearly
  umbilical and quasi Einstein hypersurfaces   We prove that, for every closed (not necessarily convex) hypersurface
$\Sigma$ in $\mathbb{R}^{n+1}$ and every $p>n$, the $L^p$-norm of the
trace-free part of the anisotropic second fundamental form controls from above
the $W^{2,p}$-closeness of $\Sigma$ to the Wulff shape. In the isotropic
setting, we provide a simpler proof. This result is sharp since in the
subcritical regime $p\leq n$, the lack of convexity assumptions may lead in
general to bubbling phenomena. Moreover, we obtain a stability theorem for
quasi Einstein (not necessarily convex) hypersurfaces and we improve the
quantitative estimates in the convex setting.

3
The categories of this paper are: physics
5
The categories of this paper are: gr-qc
25
The categories of this paper are: patt-sol
4
The categories of this paper are: cond-mat
31
The categories of this paper are: ao-sci
16
The categories of this paper are: stat
13
The categories of this paper are: quant-ph
14
The categories of this paper are: math-ph
32
The categories of this paper are: atom-ph
22
The categories of this paper are: chao-dyn
35
The categories of this paper are: mtrl-th
10
The categories of this paper are: q-bio
37
The categories of this paper are: supr-con
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The categories of this paper are: hep-ex
36
The categories of this paper are: cmp-lg
28
The categories of this paper are: alg-geom