Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Estimates for eigenvalues of Lr operator on self-shrinkers   Let $x: M\rightarrow \mathbb{R}^{N}$ be an $n$-dimensional compact
self-shrinker in $\mathbb{R}^N$ with smooth boundary $\partial\Omega$. In this
paper, we study eigenvalues of the operator $\mathcal{L}_r$ on $M$, where
$\mathcal{L}_r$ is defined by $$\mathcal{L}_r=e^{\frac{|x|^2}{2}}{\rm
div}(e^{-\frac{|x|^2}{2}}T^r\nabla\cdot)$$ with $T^r$ denoting a positive
definite (0,2)-tensor field on $M$. We obtain "universal" inequalities for
eigenvalues of the operator $\mathcal{L}_r$. These inequalities generalize the
result of Cheng and Peng in \cite{ChengPeng2013}.
  Furthermore, we also consider the case that equalities occur.

19
The categories of this paper are: eess
0
The categories of this paper are: hep-ph
30
The categories of this paper are: q-alg
24
The categories of this paper are: dg-ga
22
The categories of this paper are: chao-dyn
12
The categories of this paper are: nucl-th
37
The categories of this paper are: supr-con
1
The categories of this paper are: cs
8
The categories of this paper are: hep-ex
34
The categories of this paper are: chem-ph
9
The categories of this paper are: nlin
21
The categories of this paper are: adap-org
6
The categories of this paper are: astro-ph
20
The categories of this paper are: acc-phys
25
The categories of this paper are: patt-sol
29
The categories of this paper are: funct-an