A geometric study of Wasserstein spaces: isometric rigidity in negative curvature

The dynamic pace of development of automated testing requires the answer to the question “can we all automate?” What is the role of manual testers in modern software

In VADA [21], all of format transformation, source selection, matching, mapping and data repair are informed by evidence in the form of the data context [20], instance values that

In any 3-dimensional warped product space, the only possible embedded strictly convex surface with constant scalar curvature is the slice sphere provided that the embedded

We will establish a local Li-Yau’s estimate for weak solutions of the heat equation and prove a sharp Yau’s gradient gradient for harmonic functions on metric measure spaces, under

In this paper, we introduce a new notion for lower bounds of Ricci curvature on Alexandrov spaces, and extend Cheeger–Gromoll splitting theorem and Cheng’s maximal diameter theorem

In 1979, Ejiri [Eji79] obtained the following rigidity theorem for n( ≥ 4)- dimensional oriented compact simply connected minimal submanifolds with pinched Ricci curvatures in

To establish these theorems we will prove some rigidity results for Riemannian submersions, eg., any Riemannian submersion with complete flat total space and compact base in fact

To show that the exotic isometry flow of W 2 ( R ) is exceptional, let us consider the higher-dimensional case : there are isometries of W 2 ( R n ) that fix pointwise the set of