TITLE

# Meromorphic differentials with twisted coefficients on compact Riemann surfaces

AUTHOR(S)
Yi-Hu Yang
PUB. DATE
August 2008
SOURCE
Calculus of Variations & Partial Differential Equations;Aug2008, Vol. 32 Issue 4, p411
SOURCE TYPE
DOC. TYPE
Article
ABSTRACT
We apply the Dirichletâ€™s principle to a modified energy functional on Riemann surfaces to reprove the existence of harmonic metrics with certain prescribed singularities due to Simpson, Sabbah and Biquardâ€“Boalch, and hence of differentials with twisted coefficients of the second and third kinds. As a by-product, this generalizes the classical theory of Abelian differentials on a compact Riemann surface to the case of twisted coefficients. This also proposes a more natural approach for general existence of harmonic metrics in the higher dimensional case.
ACCESSION #
31998852

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