Entire Monge-Amp\`ere equations and weighted Minkowski problems
Jacopo Ulivelli
TL;DR
This paper proves the existence of solutions to a Monge-Ampère equation related to a weighted Minkowski problem, extending classical geometric analysis to a broader weighted context.
Contribution
It introduces a new existence result for entire Monge-Ampère equations associated with weighted Minkowski problems, expanding the theoretical framework.
Findings
Existence of solutions to a weighted Monge-Ampère equation.
Extension of classical Minkowski problem to weighted setting.
Theoretical advancement in geometric analysis.
Abstract
In this short note, we prove the existence of solutions to a Monge-Amp\`ere equation of entire type derived by a weighted version of the classical Minkowski problem.
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Taxonomy
TopicsGeometry and complex manifolds · Geometric Analysis and Curvature Flows