Two Kneser–Poulsen-type inequalities in planes of constant curvature

Isoperimetric-type inequalities on constant curvature manifolds

By exploiting optimal transport theory on Riemannian manifolds and adapting Gromov’s proof of the isoperimetric inequality in the Euclidean space, we prove an isoperimetric-type inequality on simply connected constant curvature manifolds.

Bonnesen-type inequalities for surfaces of constant curvature

A Bonnesen-type inequality is a sharp isoperimetric inequality that includes an error estimate in terms of inscribed and circumscribed regions. A kinematic technique is used to prove a Bonnesen-type inequality for the Euclidean sphere (having constant Gauss curvature κ > 0) and the hyperbolic plane (having constant Gauss curvature κ < 0). These generalized inequalities each converge to the clas...

Two-Dimensional Finsler Metrics with Constant Curvature

We construct infinitely many two-dimensional Finsler metrics on S 2 and D 2 with non-zero constant flag curvature. They are all not locally projectively flat.

Hypersurfaces with Constant Mean Curvature in a Lorentzian Space Form

integral inequalities for submanifolds of hessian manifolds with constant hessian sectional curvature

in this paper, we obtain two intrinsic integral inequalities of hessian manifolds.