A remark on the second order estimates for the quaternionic Calabi-Yau problem on hyperk\"ahler manifolds

TL;DR

This paper provides a simplified proof for second order estimates in the quaternionic Calabi-Yau problem on hyperk"ahler manifolds, refining previous results by Dinew and Sroka.

Contribution

It introduces a streamlined argument to establish second order estimates, enhancing understanding of the quaternionic Calabi-Yau problem.

Findings

Simplified proof of second order estimate

Clarification of techniques for quaternionic Monge-Ampère equations

Potential for broader application in hyperk"ahler geometry

Abstract

We revisit the second order estimate for solutions to the quaternionic Calabi-Yau problem on hyperk\"ahler manifolds, originally established by Dinew and Sroka. In this note, we present a simplified argument to derive the estimate.