Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A Riemannian Corollary of Helly's Theorem   We introduce a notion of halfspace for Hadamard manifolds that is natural in
the context of convex optimization. For this notion of halfspace, we generalize
a classic result of Gr\"unbaum, which itself is a corollary of Helly's theorem.
Namely, given a probability distribution on the manifold, there is a point for
which all halfspaces based at this point have at least $\frac{1}{n+1}$ of the
mass. As an application, the gradient oracle complexity of convex optimization
is polynomial in the parameters defining the problem.

13
The categories of this paper are: quant-ph
16
The categories of this paper are: stat
9
The categories of this paper are: nlin
27
The categories of this paper are: comp-gas
37
The categories of this paper are: supr-con
34
The categories of this paper are: chem-ph
4
The categories of this paper are: cond-mat
28
The categories of this paper are: alg-geom
36
The categories of this paper are: cmp-lg
22
The categories of this paper are: chao-dyn
35
The categories of this paper are: mtrl-th
20
The categories of this paper are: acc-phys
11
The categories of this paper are: hep-lat
6
The categories of this paper are: astro-ph
25
The categories of this paper are: patt-sol
30
The categories of this paper are: q-alg