Fractional Poincar\'e inequality with finite total $Q$-curvature

TL;DR

This paper establishes fractional Poincaré inequalities on conformally flat manifolds with finite total Q-curvature, revealing new insights into the geometric analysis of noncompact manifolds.

Contribution

It introduces novel fractional Poincaré inequalities in the context of conformally flat manifolds with finite total Q-curvature, expanding understanding of geometric inequalities.

Findings

Proved fractional Poincaré inequalities on specific manifolds

Connected Q-curvature properties with fractional inequalities

Highlighted new geometric aspects of noncompact manifolds

Abstract

In this paper, we prove several Poincar\'e inequalities of fractional type on conformally flat manifolds with finite total Q-curvature. This shows a new aspect of the $Q$-curvature on noncompact complete manifolds.