Monotonicity Formulas for Bakry-Emery Ricci Curvature
Bingyu Song, Guofang Wei, and Guoqiang Wu
TL;DR
This paper develops new monotonicity formulas for manifolds with nonnegative Bakry-Emery Ricci curvature, extending previous results and providing tools for geometric analysis in weighted manifolds.
Contribution
It introduces several new families of monotonicity formulas specifically for manifolds with nonnegative Bakry-Emery Ricci curvature, expanding the theoretical framework.
Findings
Derived multiple new monotonicity formulas
Extended previous formulas to Bakry-Emery Ricci curvature setting
Provides tools for further geometric analysis
Abstract
Motivated and inspired by the recent work of Colding [5] and Colding-Minicozzi [6] we derive several families of monotonicity formulas for manifolds with nonnegative Bakry-Emery Ricci curvature, extending the formulas in [5, 6].
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Taxonomy
TopicsGeometric Analysis and Curvature Flows · Advanced Differential Geometry Research · Geometry and complex manifolds