36 citations · 112 across the 21 of their papers we have counts for
8 papers · 1 filter
Twisted Kähler-Einstein metrics
Julius Ross, Gábor Székelyhidi
We prove an existence result for twisted Kähler-Einstein metrics, assuming an appropriate twisted K-stability condition. An improvement over earlier results is that certain non-neg…
K-stability for Kähler Manifolds
Ruadhaí Dervan, Julius Ross
We formulate a notion of K-stability for Kähler manifolds, and prove one direction of the Yau-Tian-Donaldson conjecture in this setting. More precisely, we prove that the Mabuchi f…
Quantization of Hitchin's equations for Higgs Bundles I
Mario Garcia-Fernandez, Julien Keller, Julius Ross
We provide an algebraic framework for quantization of Hermitian metrics that are solutions of the Hitchin equation for Higgs bundles over a projective manifold. Using Geometric Inv…
Balanced metrics on twisted Higgs Bundles
Mario Garcia-Fernandez, Julius Ross
A twisted Higgs bundle on a Kähler manifold is a pair consisting of a holomorphic vector bundle and a holomorphic bundle morphism for som…
Asymptotics of Partial Density Functions for Divisors
Julius Ross, Michael Singer
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…
Limits of balanced metrics on vector bundles and polarised manifolds
Mario Garcia-Fernandez, Julius Ross
We consider a notion of balanced metrics for triples (X,L,E) which depend on a parameter α, where X is smooth complex manifold with an ample line bundle L and E is a holomorphic ve…