Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Geodesic stability, the space of rays, and uniform convexity in Mabuchi
  geometry   We establish the essentially optimal form of Donaldson's geodesic stability
conjecture regarding existence of constant scalar curvature K\"ahler metrics.
We carry this out by exploring in detail the metric geometry of Mabuchi
geodesic rays, and the uniform convexity properties of the space of K\"ahler
metrics.

32
The categories of this paper are: atom-ph
23
The categories of this paper are: solv-int
0
The categories of this paper are: hep-ph
8
The categories of this paper are: hep-ex
17
The categories of this paper are: q-fin
33
The categories of this paper are: plasm-ph
10
The categories of this paper are: q-bio
25
The categories of this paper are: patt-sol
9
The categories of this paper are: nlin
13
The categories of this paper are: quant-ph
5
The categories of this paper are: gr-qc
7
The categories of this paper are: hep-th
15
The categories of this paper are: nucl-ex
6
The categories of this paper are: astro-ph
11
The categories of this paper are: hep-lat
27
The categories of this paper are: comp-gas