Corrigendum to: “A lattice‐point problem in hyperbolic space”

The Double Bubble Problem in Spherical Space and Hyperbolic Space

A Boundary Value Problem in the Hyperbolic Space

The Double Bubble Problem in Spherical and Hyperbolic Space

The Weyl Problem with Nonnegative Gauss Curvature in Hyperbolic Space

In this paper, we discuss the isometric embedding problem in hyperbolic space with nonnegative extrinsic curvature. We prove a priori bounds for the trace of the second fundamental form H and extend the result to ndimensions. We also obtain an estimate for the gradient of the smaller principal curvature in 2 dimensions.

A Solution to the Lower Dimensional Busemann-petty Problem in the Hyperbolic Space

The lower dimensional Busemann-Petty problem asks whether origin symmetric convex bodies in R with smaller volume of all k-dimensional sections necessarily have smaller volume. As proved by Bourgain and Zhang, the answer to this question is negative if k > 3. The problem is still open for k = 2, 3. In this article we formulate and completely solve the lower dimensional Busemann-Petty problem in...