Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Determination of isometric real-analytic metric and spectral invariants
  for elastic Dirichlet-to-Neumann map on Riemannian manifolds   For a compact Riemannian manifold $(\Omega, g)$ with smooth boundary
$\partial \Omega$, we explicitly give local representation and full symbol
expression for the elastic Dirichlet-to-Neumann map $\Xi_g$ by factorizing an
equivalent elastic equation. We prove that for a strong convex or extendable
real-analytic manifold $\Omega$ with boundary, the elastic Dirichlet-to-Neumann
map $\Xi_g$ uniquely determines metric $g$ of $\Omega$ in the sense of
isometry. We also give a procedure by which we can explicitly calculate all
coefficients $a_0, a_1 \cdots, a_{n-1}$ of the asymptotic expansion
$\sum_{k=1}^\infty e^{-t \tau_k}\sim \sum\limits_{m=0}^{n-1} a_m t^{m+1-n}
+o(1)$ as $t\to 0^+$, where $\tau_k$ is the $k$-th eigenvalue of the elastic
Dirichlet-to-Neumann map (i.e., $k$-th elastic Steklov eigenvalue). The
coefficients $a_m$ are spectral invariants and provide precise information for
the boundary volume ${\mbox{vol}} (\partial \Omega)$ of the elastic medium
$\Omega$ and the total mean curvature as well as other total curvatures of the
boundary $\partial \Omega$. These conclusions give answer to two open problems.

37
The categories of this paper are: supr-con
33
The categories of this paper are: plasm-ph
19
The categories of this paper are: eess
26
The categories of this paper are: bayes-an
8
The categories of this paper are: hep-ex
1
The categories of this paper are: cs
13
The categories of this paper are: quant-ph
7
The categories of this paper are: hep-th
12
The categories of this paper are: nucl-th
29
The categories of this paper are: funct-an
0
The categories of this paper are: hep-ph
36
The categories of this paper are: cmp-lg
25
The categories of this paper are: patt-sol
11
The categories of this paper are: hep-lat
10
The categories of this paper are: q-bio
21
The categories of this paper are: adap-org