The extrinsic curvature of entire minimal graphs in $\H^2\times\R$

TL;DR

This paper provides an optimal estimate for the extrinsic curvature of entire minimal graphs in the hyperbolic plane cross the real line, advancing understanding of their geometric properties.

Contribution

It introduces the first optimal curvature estimate specifically for entire minimal graphs in , a significant step in hyperbolic geometry research.

Findings

Established an optimal extrinsic curvature bound

Enhanced understanding of minimal surface geometry in hyperbolic spaces

Potential applications in geometric analysis and mathematical physics

Abstract

We obtain an optimal estimate for the extrinsic curvature of an entire minimal graph in $\H^2\times\R$, $\H^2$ the hyperbolic plane.