Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Convexity of Hypersurfaces in Spherical Spaces   A spherical set is called convex if for every pair of its points there is at
least one minimal geodesic segment that joins these points and lies in the set.
We prove that for n >= 3 a complete locally-convex (topological) immersion of a
connected (n-1)-manifold into the n-sphere is a surjection onto the boundary of
a convex set.

26
The categories of this paper are: bayes-an
20
The categories of this paper are: acc-phys
5
The categories of this paper are: gr-qc
14
The categories of this paper are: math-ph
29
The categories of this paper are: funct-an
22
The categories of this paper are: chao-dyn
36
The categories of this paper are: cmp-lg
3
The categories of this paper are: physics
32
The categories of this paper are: atom-ph
17
The categories of this paper are: q-fin
19
The categories of this paper are: eess
15
The categories of this paper are: nucl-ex
30
The categories of this paper are: q-alg
7
The categories of this paper are: hep-th
37
The categories of this paper are: supr-con
4
The categories of this paper are: cond-mat