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arXiv · 2201.01150

Pluripotential Chern-Ricci Flows

Quang-Tuan Dang
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Abstract

Extending a recent theory developed on compact K\"ahler manifolds by Guedj-Lu-Zeriahi and the author, we define and study pluripotential solutions to degenerate parabolic complex Monge-Amp\`ere equations on compact Hermitian manifolds. Under natural assumptions on the Cauchy boundary data, we show that the pluripotential solution is semi-concave in time and continuous in space and that such a solution is unique. We also establish a partial regularity of such solutions under some extra assumptions of the densities and apply it to prove the existence and uniqueness of the weak Chern-Ricci flow on complex compact varieties with log terminal singularities.

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BibTeXRIS

Quang-Tuan Dang. 2022-01-03. Pluripotential Chern-Ricci Flows. https://doi.org/10.1512/iumj.2024.73.60000

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