Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Geometry of K\"ahler Metrics and Foliations by Holomorphic Discs   The purpose of this paper is to establish a completely new partial regularity
theory on certain homogeneous complex Monge-Ampere equations. Our partial
regularity theory will be obtained by studying foliations by holomorphic curves
and and their relations to homogeneous complex Monge-Ampere equations. As
applications, we will prove the uniqueness of extremal K\"ahler metrics and
give an necessary condition for existence of extremal K\"ahler metrics. Further
applications will be discussed in our forthcoming papers.

18
The categories of this paper are: econ
21
The categories of this paper are: adap-org
23
The categories of this paper are: solv-int
1
The categories of this paper are: cs
9
The categories of this paper are: nlin
30
The categories of this paper are: q-alg
16
The categories of this paper are: stat
12
The categories of this paper are: nucl-th
19
The categories of this paper are: eess
10
The categories of this paper are: q-bio
32
The categories of this paper are: atom-ph
17
The categories of this paper are: q-fin
11
The categories of this paper are: hep-lat
31
The categories of this paper are: ao-sci
14
The categories of this paper are: math-ph
4
The categories of this paper are: cond-mat