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arXiv · 2311.11612

Balanced metrics for extremal K\"ahler metrics and Fano manifolds

Yoshinori Hashimoto
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Abstract

The first three sections of this paper are a survey of the author's work on balanced metrics and stability notions in algebraic geometry. The last section is devoted to proving the well-known result that a geodesically convex function on a complete Riemannian manifold admits a critical point if and only if its asymptotic slope at infinity is positive, where we present a proof which relies only on the Hopf--Rinow theorem and extends to locally compact complete length metric spaces.

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BibTeXRIS

Yoshinori Hashimoto. 2023-11-20. Balanced metrics for extremal K\"ahler metrics and Fano manifolds. https://doi.org/10.1007/978-981-99-9506-6_5

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