Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Ramified local isometric embeddings of singular Riemannian metrics   In this paper, we are concerned with the existence of local isometric
embeddings into Euclidean space for analytic Riemannian metrics $g$, defined on
a domain $U\subset \mathbf{R}^n$, which are singular in the sense that the
determinant of the metric tensor is allowed to vanish at an isolated point (say
the origin). Specifically, we show that, under suitable technical assumptions,
there exists a local analytic isometric embedding $u$ from $(U',\Pi^*g)$ into
Euclidean space $\mathbf{E}^{(n^2+3n-4)/2}$, where $\Pi:U' \to
U\backslash\{0\}$ is a finite Riemannian branched cover of a deleted
neighborhood of the origin. Our result can thus be thought of as a
generalization of the classical Cartan-Janet Theorem to the singular setting in
which the metric tensor is degenerate at an isolated point. Our proof uses
Leray's ramified Cauchy-Kovalevskaya Theorem for analytic differential systems,
in the form obtained by Choquet-Bruhat for non-linear systems.

11
The categories of this paper are: hep-lat
24
The categories of this paper are: dg-ga
12
The categories of this paper are: nucl-th
19
The categories of this paper are: eess
32
The categories of this paper are: atom-ph
13
The categories of this paper are: quant-ph
9
The categories of this paper are: nlin
15
The categories of this paper are: nucl-ex
4
The categories of this paper are: cond-mat
25
The categories of this paper are: patt-sol
29
The categories of this paper are: funct-an
10
The categories of this paper are: q-bio
26
The categories of this paper are: bayes-an
18
The categories of this paper are: econ
34
The categories of this paper are: chem-ph
27
The categories of this paper are: comp-gas