In this paper, we prove a family of identities for smooth closed and strictly convex
hypersurfaces in the sphere and hyperbolic/de Sitter space. As applications, we prove …

The classical Minkowski inequality in the Euclidean space provides a lower bound on the
total mean curvature of a hypersurface in terms of the surface area, which is optimal on …

The long-time existence and umbilicity estimates for compact, graphical solutions to
expanding curvature flows are deduced in Riemannian warped products of a real interval …

We employ curvature flows without global terms to seek strictly convex, spacelike solutions
of a broad class of elliptic prescribed curvature equations in the simply connected …

To a real n-dimensional vector space V and a smooth, symmetric function f defined on the n-
dimensional Euclidean space we assign an associated operator function F defined on linear …

We construct closed, embedded, ancient mean curvature flows in each dimension with the
topology of. These examples are not mean convex and not solitons. They are constructed by …

An important set of theorems in geometric analysis consists of constant rank theorems for a
wide variety of curvature problems. In this paper, for geometric curvature problems in …

We propose a new bilinear Hirota equation for-functions associated with the root lattice that
provides a “lens” generalisation of the-functions for the elliptic discrete Painlevé equation …

We obtain a differential Harnack inequality for anisotropic curvature flow of convex
hypersurfaces in Euclidean space with its speed given by a curvature function of …

This short note is a mostly expository article examining negatively curved three-manifolds.
We look at some rigidity properties related to isometric embeddings into Minkowski space …