ACF-Monotonicity Formula on RCD(0,N) Metric Measure Cones
Lin Sitan
TL;DR
This paper extends the ACF-monotonicity formula to RCD(0,N) metric measure cones and uses it to establish a rigidity result, advancing the understanding of geometric analysis on these spaces.
Contribution
It introduces an extension of the ACF-monotonicity formula to RCD(0,N) cones and applies it to prove a new rigidity theorem for these spaces.
Findings
Extension of ACF-monotonicity formula to RCD(0,N) cones
Rigidity result for RCD(0,N) metric measure cones
Advancement in geometric analysis on metric measure spaces
Abstract
The ACF-monotonicity formula is a powerful tool in the study of two-phase free boundary problems, which was introduced by Alt, Caffarelli, and Friedman[1]. In this paper, we extend it to RCD(0,N) metric measure cones. As an application, we give a rigidity result for RCD(0,N) metric measure cones.
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Taxonomy
TopicsMathematical Inequalities and Applications · Advanced Optimization Algorithms Research · Matrix Theory and Algorithms