Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Asymptotic properties of extremal K\"ahler metrics of Poincar\'e type   Consider a compact K\"ahler manifold X with a simple normal crossing divisor
D, and define Poincar\'e type metrics on X\D as K\"ahler metrics on X\D with
cusp singularities along D. We prove that the existence of a constant scalar
curvature (resp. an extremal) Poincar\'e type K\"ahler metric on X\D implies
the existence of a constant scalar curvature (resp. an extremal) K\"ahler
metric, possibly of Poincar\'e type, on every component of D. We also show that
when the divisor is smooth, the constant scalar curvature/extremal metric on
X\D is asymptotically a product near the divisor.

32
The categories of this paper are: atom-ph
15
The categories of this paper are: nucl-ex
28
The categories of this paper are: alg-geom
17
The categories of this paper are: q-fin
23
The categories of this paper are: solv-int
35
The categories of this paper are: mtrl-th
6
The categories of this paper are: astro-ph
37
The categories of this paper are: supr-con
12
The categories of this paper are: nucl-th
4
The categories of this paper are: cond-mat
18
The categories of this paper are: econ
9
The categories of this paper are: nlin
34
The categories of this paper are: chem-ph
19
The categories of this paper are: eess
3
The categories of this paper are: physics
13
The categories of this paper are: quant-ph