Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Existence of constant mean curvature 2-spheres in Riemannian 3-spheres   We prove the existence of branched immersed constant mean curvature 2-spheres
in an arbitrary Riemannian 3-sphere for almost every prescribed mean curvature,
and moreover for all prescribed mean curvatures when the 3-sphere is positively
curved. To achieve this, we develop a min-max scheme for a weighted Dirichlet
energy functional. There are three main ingredients in our approach: a
bi-harmonic approximation procedure to obtain compactness of the new
functional, a derivative estimate of the min-max values to gain energy upper
bounds for min-max sequences for almost every choice of mean curvature, and a
Morse index estimate to obtain another uniform energy bound required to reach
the remaining constant mean curvatures in the presence of positive curvature.

31
The categories of this paper are: ao-sci
34
The categories of this paper are: chem-ph
24
The categories of this paper are: dg-ga
20
The categories of this paper are: acc-phys
30
The categories of this paper are: q-alg
32
The categories of this paper are: atom-ph
12
The categories of this paper are: nucl-th
37
The categories of this paper are: supr-con
26
The categories of this paper are: bayes-an
36
The categories of this paper are: cmp-lg
22
The categories of this paper are: chao-dyn
17
The categories of this paper are: q-fin
6
The categories of this paper are: astro-ph
23
The categories of this paper are: solv-int
0
The categories of this paper are: hep-ph
4
The categories of this paper are: cond-mat