Generalized Donaldson's functionals and related nonlinear partial differential equations

Abstract

In this paper, we introduce a family of generalized Donaldson's functional on holomorphic vector bundles, whose Euler-Lagrange equations are a vector bundle version of the complex $k$-Hessian equations. We also discuss the uniqueness of solutions to these equations.

References in corpus (1)

• Kobayashi-Hitchin correspondence for tame harmonic bundles and an application