Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Toric K\"ahler-Einstein metrics and convex compact polytopes   We show that any compact convex simple lattice polytope is the moment
polytope of a K\"ahler-Einstein orbifold, unique up to orbifold covering and
homothety. We extend the Wang-Zhu Theorem \cite{WZ} giving the existence of a
K\"ahler-Ricci soliton on any toric monotone manifold on any compact convex
simple labelled polytope satisfying the combinatoric condition corresponding to
monotonicity. We obtain that any compact convex simple polytope $P\subset
\bR^n$ admits a set of inward normals, unique up to dilatation, such that there
exists a symplectic potential satisfying the Guillemin boundary condition (with
respect to these normals) and the K\"ahler-Einstein equation on $P\times
\bR^n$. We interpret our result in terms of existence of singular
K\"ahler-Einstein metrics on toric manifolds.

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The categories of this paper are: solv-int
14
The categories of this paper are: math-ph
32
The categories of this paper are: atom-ph
7
The categories of this paper are: hep-th
16
The categories of this paper are: stat
25
The categories of this paper are: patt-sol
10
The categories of this paper are: q-bio
13
The categories of this paper are: quant-ph
26
The categories of this paper are: bayes-an
5
The categories of this paper are: gr-qc
36
The categories of this paper are: cmp-lg
15
The categories of this paper are: nucl-ex
6
The categories of this paper are: astro-ph
31
The categories of this paper are: ao-sci
34
The categories of this paper are: chem-ph
35
The categories of this paper are: mtrl-th