New equation on the low dimensional Calabi-Yau metrics
Dmitry Egorov
TL;DR
This paper introduces a novel equation on compact Kähler manifolds that characterizes Calabi-Yau metrics, offering an alternative to the classical Monge-Ampère equation.
Contribution
It proposes a new mathematical equation for Calabi-Yau metrics, expanding the tools available for studying these geometric structures.
Findings
New equation characterizes Calabi-Yau metrics.
Differentiates from the classical Monge-Ampère equation.
Provides potential new methods for geometric analysis.
Abstract
In this paper we introduce a new equation on the compact Kahler manifolds. Solution of this equation corresponds to the Calabi-Yau metric. New equation differs from the Monge--Ampere equation considered by Calabi and Yau.
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Taxonomy
TopicsGeometry and complex manifolds · Geometric Analysis and Curvature Flows · Algebraic Geometry and Number Theory