A maximum principle for hermitian (and other) metrics

TL;DR

This paper proves that for homomorphisms of hermitian holomorphic Hilbert bundles decreasing curvature, the pointwise norm is a plurisubharmonic function, providing a maximum principle in this geometric setting.

Contribution

It establishes a maximum principle for the pointwise norm of curvature-decreasing homomorphisms of hermitian holomorphic Hilbert bundles.

Findings

Pointwise norm is plurisubharmonic under curvature decrease.

Provides a maximum principle for hermitian bundle homomorphisms.

Extends classical maximum principles to infinite-dimensional bundle settings.

Abstract

We consider homomorphisms of hermitian holomorphic Hilbert bundles. Assuming the homomorphism decreases curvature, we prove that its pointwise norm is plurisubharmonic.