When optimal transport meets information geometry
G Khan, J Zhang - Information Geometry, 2022 - Springer
Abstract Information geometry and optimal transport are two distinct geometric frameworks
for modeling families of probability measures. During the recent years, there has been a …
for modeling families of probability measures. During the recent years, there has been a …
A hall of statistical mirrors
G Khan, J Zhang - arXiv preprint arXiv:2109.13809, 2021 - arxiv.org
The primary objects of study in information geometry are statistical manifolds, which are
parametrized families of probability measures, induced with the Fisher-Rao metric and a pair …
parametrized families of probability measures, induced with the Fisher-Rao metric and a pair …
An Illustrated Introduction to the Ricci Flow
G Khan - arXiv preprint arXiv:2201.04923, 2022 - arxiv.org
The Ricci flow is one of the most important topics in differential geometry, and a central focus
of modern geometric analysis. In this paper, we give an illustrated introduction to the subject …
of modern geometric analysis. In this paper, we give an illustrated introduction to the subject …
Non-existence of complete Kähler metric of negatively pinched holomorphic sectional curvature
G Cho - Complex Analysis and its Synergies, 2023 - Springer
We prove a theorem which provides a sufficient condition for the non-existence of a
complete Kähler–Einstein metric of negative scalar curvature of which holomorphic sectional …
complete Kähler–Einstein metric of negative scalar curvature of which holomorphic sectional …
Positively curved K\" ahler metrics on tube domains and their applications to optimal transport
G Khan, J Zhang, F Zheng - arXiv preprint arXiv:2001.06155, 2020 - arxiv.org
In this article, we study a class of K\" ahler manifolds defined on tube domains in $\mathbb
{C}^ n $, and in particular those which have $ O (n)\times\mathbb {R}^ n $ symmetry. For …
{C}^ n $, and in particular those which have $ O (n)\times\mathbb {R}^ n $ symmetry. For …