A functional inequality between Hessians in spaces with non-zero curvature

TL;DR

This paper extends a known functional inequality relating the Hessians of the square root and logarithm of positive functions to spaces with non-zero curvature, broadening its applicability.

Contribution

It introduces a new version of the functional inequality applicable in curved spaces, expanding previous results limited to flat geometries.

Findings

Proves a functional inequality in curved spaces.

Generalizes previous flat-space inequalities.

Enhances understanding of Hessian relations in non-zero curvature.

Abstract

A version of the recent functional inequality between the Hessians of the square root and the logarithm of positive functions is proven in spaces with non-zero curvature.