C^0 estimates for Hessian quotient equations on HKT manifolds
Li Chen
TL;DR
This paper establishes $C^0$ estimates for solutions to Hessian quotient equations on HKT manifolds, advancing understanding of these equations without requiring extra assumptions on the hypercomplex structure.
Contribution
It provides a novel $C^0$ estimate for Hessian quotient equations on HKT manifolds using the cone condition directly, without additional structural assumptions.
Findings
Established $C^0$ estimates for solutions
Applied cone condition directly in the proof
No extra assumptions on hypercomplex structure needed
Abstract
We show the estimate for solutions to Hessian quotient equations on hyperK\"ahler with torsion manifolds without any additional assumption on its hypercomplex structure by a clever use of the cone condition directly.
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Taxonomy
TopicsGeometry and complex manifolds · Geometric Analysis and Curvature Flows · Black Holes and Theoretical Physics