Complex Brunn–minkowski Theory and Positivity of Vector Bundles

Abstract

This is a survey of results on positivity of vector bundles, inspired by the Brunn-Minkowski and Prékopa theorems. Applications to complex analysis, Kähler geometry and algebraic geometry are also discussed. R ue −φ(x) dx = 0, 1

Interpolation, Prekopa and Brunn-Minkowski for $F$-subharmonicity

“…The complex version of the Brunn-Minkowski and Preokopa Theorems is a theme in work of Berndtsson [3][4][5][6][7][8] where it has in particular found applications to positivity of vector bundles and Fano manifolds (see also [28] for a survey). This has since been taken up by others (e.g.…”