Monotonicity formulae and vanishing theorems

Jintang Li

Vol. 281 (2016), No. 1, 125–136

DOI: 10.2140/pjm.2016.281.125

Abstract

We study Cartan–Hadamard manifolds with pinching conditions. Using the stress-energy tensor, we establish some monotonicity formulae for vector bundle-valued $p$-forms and pluriharmonic maps between Kähler manifolds. Some vanishing theorems follow immediately from the monotonicity formulae under suitable growth conditions on the energy of $p$-forms and pluriharmonic maps.

Keywords

monotonicity formulae, Kähler manifolds, $p$-forms, pluriharmonic maps

Mathematical Subject Classification 2010

Primary: 53C43

Secondary: 53C55

Milestones

Received: 27 January 2015

Revised: 25 May 2015

Accepted: 8 July 2015

Published: 9 February 2016