Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A convergence framework for optimal transport on the sphere   We consider a PDE approach to numerically solving the optimal transportation
problem on the sphere. We focus on both the traditional squared geodesic cost
and a logarithmic cost, which arises in the reflector antenna design problem.
At each point on the sphere, we replace the surface PDE with a generalized
Monge-Amp\`ere type equation posed on the tangent plane using normal
coordinates. The resulting nonlinear PDE can then be approximated by any
consistent, monotone scheme for generalized Monge-Amp\`ere type equations on
the plane. Existing techniques for proving convergence do not immediately apply
because the PDE lacks both a comparison principle and a unique solution, which
makes it difficult to produce a stable, well-posed scheme. By augmenting this
discretization with an additional term that constrains the solution gradient,
we obtain a strong form of stability. A modification of the Barles-Souganidis
convergence framework then establishes convergence to the mean-zero solution of
the original PDE.

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
28
The categories of this paper are: alg-geom
33
The categories of this paper are: plasm-ph
14
The categories of this paper are: math-ph
27
The categories of this paper are: comp-gas
6
The categories of this paper are: astro-ph
5
The categories of this paper are: gr-qc
8
The categories of this paper are: hep-ex
37
The categories of this paper are: supr-con
31
The categories of this paper are: ao-sci
10
The categories of this paper are: q-bio
32
The categories of this paper are: atom-ph
26
The categories of this paper are: bayes-an
30
The categories of this paper are: q-alg