Geodesics in the space of Kähler metrics

By László Lempert, L. Vivas. 2011

76 citations recorded by the source corpus.

Let (X,ω) be a compact Kähler manifold. As discovered in the late 1980s by Mabuchi, the set H0 of Kähler forms cohomologous to ω has the natural structure of an infinite dimensional Riemannian manifold. We address the question whether any two points in H0 can be connected by a smooth geodesic, and show that the answer, in general, is “no”.

Subfields: Applied Mathematics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/fed54960b5932a6d40eae5e7e3bae770e0c03b5e

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In Applied Mathematics

1. B. Berndtsson
2. Robert J. Berman
3. Chi Li
4. Song Sun
5. Simon Donaldson
6. László Lempert
7. G. Tian
8. Tam'as Darvas

In Geometry and Topology

1. B. Berndtsson
2. Robert J. Berman
3. Chi Li
4. Song Sun
5. Simon Donaldson
6. László Lempert
7. Junyan Cao
8. G. Tian

In Mathematical Physics

1. B. Berndtsson
2. Robert J. Berman

Citations in the corpus

• On the singularity type of full mass currents in big cohomology classes (2016, unknown): “When θ is also nef, by adapting the proof of Chen [Che00] (see [Bou12]), we expect that a similar regularity result still holds in the ample locus of {θ}.”
• A Brunn–Minkowski type inequality for Fano manifolds and some uniqueness theorems in Kähler geometry (2013, background): “This solution does in general not need to be smooth (see [13],[23], [11]), but Chen’s theorem asserts that we can find a solution that has all mixed complex derivatives bounded, i e∂∂̄t,Xφ is bounded onX × Ω.”