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Balanced metrics on twisted Higgs bundles
(SpringerMathematische Annalen, 2016)
Asymptotics of Partial Density Functions for Divisors
(SpringerThe Journal of Geometric Analysis, 2016-09-19)
We study the asymptotic behaviour of the partial density function associated to sections of a positive hermitian line bundle that vanish to a particular order along a fixed divisor $Y$ . Assuming the data in question is ...
Envelopes of positive metrics with prescribed singularities
(Université Paul Sabatier, ToulouseAnnales de la Faculté des Sciences de Toulouse, 2016)
We investigate envelopes of positive metrics with a prescribed singularity type. First we generalise work of Berman to this setting, proving C$^{1,1}$ regularity of such envelopes, showing their Monge-Ampère measure is ...