The Weighted Ambient Metric
Jeffrey S. Case, Ayush Khaitan
TL;DR
This paper establishes the existence and uniqueness of weighted ambient and Poincaré metrics for smooth metric measure spaces, advancing the theoretical understanding of geometric structures in weighted settings.
Contribution
It introduces the concepts of weighted ambient and Poincaré metrics and proves their existence and uniqueness in smooth metric measure spaces.
Findings
Existence of weighted ambient metrics proven
Uniqueness of weighted ambient metrics established
Extension to weighted Poincaré metrics demonstrated
Abstract
We prove the existence and uniqueness of weighted ambient metrics and weighted Poincar\'e metrics for smooth metric measure spaces.
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Taxonomy
TopicsGeometry and complex manifolds · Geometric Analysis and Curvature Flows · Fixed Point Theorems Analysis