Approximation of weak geodesics and subharmonicity of Mabuchi energy

Long Li; Mihai Paun; Xiuxiong Chen

Approximation of weak geodesics and subharmonicity of Mabuchi energy

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arxiv 1409.7896 v1 pith:EDCASKY2 submitted 2014-09-28 math.DG math.CV

XiuXiong Chen , Long Li , Mihai Paun This is my paper · ORCID

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keywords geodesicsweakapproximationmabuchialonganalysingcontinuityconvexity

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We are analysing the convexity and continuity properties of the Mabuchi functional along weak geodesics. The key technical point in our paper is the global approximation of weak geodesics obtained via a well-chosen family of Monge-Amp\`ere equations.

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Analytic Bertini theorem II --- The local case
math.AG 2026-07 accept novelty 8.0 of 10

The local analytic Bertini theorem holds: multiplier ideal sheaves of psh functions on polydisc products restrict to fibers outside a pluripolar set.

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