On the invariance of the total Monge-Ampere volume of Hermitian metrics
Ionut Chiose
TL;DR
This paper characterizes Hermitian metrics that preserve the total Monge-Ampere volume and satisfy the comparison principle, providing new insights into their invariance properties in complex geometry.
Contribution
It offers new characterizations of Hermitian metrics invariant under the total Monge-Ampere volume and explores conditions for the comparison principle in complex Monge-Ampere theory.
Findings
Hermitian metrics that leave the total Monge-Ampere volume invariant are characterized.
Conditions under which these metrics satisfy the comparison principle are identified.
The paper provides multiple characterizations of such metrics.
Abstract
In this note, we describe the Hermitian metrics that leave the total Monge-Ampere volume invariant. In particular, we give several characterizations of the Hermitian metrics which satisfy the comparison principle for the complex Monge-Ampere operator
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Taxonomy
TopicsGeometry and complex manifolds · Geometric Analysis and Curvature Flows