Positivity of direct image bundles and convexity on the space of Kähler metrics.

By B. Berndtsson. 2006

86 citations recorded by the source corpus.

We develop some results from [4] on the positivity of direct image bundles in the particular case of a trivial fibration over a one-dimensional base. We also apply the results to study variations of Kahler metrics.

Subfields: Applied Mathematics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/94995b90f584d563b5c53a4d2370b9c6da83fc3d

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

1. Robert J. Berman
2. Xiaokui Yang
3. B. Berndtsson
4. Kefeng Liu
5. Xiaofeng Sun
6. Chi Li
7. Yanir A. Rubinstein
8. Tam'as Darvas

In Geometry and Topology

1. Robert J. Berman
2. Xiaokui Yang
3. B. Berndtsson
4. Kefeng Liu
5. Xiaofeng Sun
6. Chi Li
7. Tam'as Darvas
8. Yanir A. Rubinstein

In Mathematical Physics

1. Robert J. Berman
2. Kefeng Liu
3. Xiaofeng Sun
4. Xiaokui Yang
5. B. Berndtsson
6. Chi Li

Citations in the corpus

• A Brunn–Minkowski type inequality for Fano manifolds and some uniqueness theorems in Kähler geometry (2013, background): “In case −K X > 0, so that X is Fano, the result is a simple consequence of Hörmander’s L2-estimates, see [7] for a very short proof in this case.”
• Positivity and vanishing theorems for ample vector bundles (2010, background): “For more related results, we refer the reader to [2], [3] [4], [27], [28] and [33] and references therein.”
• Bergman kernels and equilibrium measures for line bundles over projective manifolds (2007, result): “The result should also be compared to various C1,1-results for boundary value problems for complex Monge-Ampere equations on manifolds with boundary [13], [14], intimately related to the study of the geometry of the space of Kähler metrics on a Kähler manifold (see also [31], [9] for other relations”