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arXiv · 2110.11169

On the Hessian-cscK equations

Bin Guo·Kevin Smith·Freid Tong
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Abstract

In this paper, we propose a coupled system of complex Hessian equations which generalizes the equation for constant scalar curvature K\"ahler (cscK) metrics. We show this system can be realized variationally as the Euler-Lagrange equation of a Hessian version of the Mabuchi K-energy in an infinite dimensional space of $k$-Hessian potentials, which can be seen as an infinite dimensional Riemannian manifold with negative sectional curvature. Finally, we prove an a priori $C^0$-estimate for this system which depends on the Entropy, which generalizes a fundamental result of Chen and Cheng for cscK metrics.

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Bin Guo, Kevin Smith, Freid Tong. 2021-10-21. On the Hessian-cscK equations. https://arxiv.org/abs/2110.11169

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