par Pook, Julian
Référence Geometriae dedicata, 181, 1, page (23-42)
Publication Publié, 2016-04
Article révisé par les pairs
Résumé : We investigate a generalisation of Hermitian Yang–Mills flow in which the base metric itself is allowed to depend on the time-parameter. For technical reasons we restrict our attention to the case of a holomorphic vector bundles E over compact Riemann surfaces which is assumed to be slope stable with respect to a fixed Kähler class (Formula presented.) on the base. We show that if (Formula presented.) is a family of Kähler metrics in (Formula presented.) converging to a limit metric (Formula presented.) at an exponential rate, then starting at a smooth initial Hermitian metric (Formula presented.) on E, the Hermitian Yang–Mills flow with respect to the time-dependent metric (Formula presented.) admits a unique long-time solution h(t) converging exponentially to a (Formula presented.) -Hermite–Einstein metric. The proof utilises an extension of Donadson’s techniques used to treat the case where the base metrics does not depend on the time-parameter.