29 citations · 50 across the 14 of their papers we have counts for
15 papers · 1 filter
A gluing construction of -extremal Kähler metrics and new examples of Bismut Hermitian-Einstein -folds
Vestislav Apostolov, Abdellah Lahdili, Kuan-Hui Lee +1
We present a gluing construction for a class of 6th order geometric non-linear PDE's on a Kähler manifold or orbifold, arising in the study of Bismut Hermitian Einstein complex …
From Calabi's extremal metrics to scalar-flat Kähler cones
Vestislav Apostolov, Abdellah Lahdili, Chung-Ming Pan
We prove that for any smooth polarized complex -dimensional manifold which admits an extremal Kähler metric in , and for any integer large enough (in te…
Pluriclosed 3-folds with vanishing Bismut Ricci form: General theory in the quasi-regular case
Vestislav Apostolov, Abdellah Lahdili, Kuan-Hui Lee
We study compact complex -dimensional non-Kähler Bismut Ricci flat pluriclosed Hermitian manifolds (BHE) via their dimensional reduction to a special Kähler geometry in complex…
The CR Yamabe invariant and constant scalar curvature Sasaki metrics
Abdellah Lahdili, Eveline Legendre, Carlo Scarpa
We propose a new approach to the existence of constant transversal scalar curvature Sasaki structures drawing on ideas and tools from the CR Yamabe problem, establishing a link bet…
Weighted cscK metric (II): the continuity method
Eleonora Di Nezza, Simon Jubert, Abdellah Lahdili
In this paper we investigate the existence of metrics with weighted constant scalar curvature (wcscK for short) on a compact Kähler manifold : this notion include constant scala…
From Kähler Ricci solitons to Calabi-Yau Kähler cones
Vestislav Apostolov, Abdellah Lahdili, Eveline Legendre
We show that if is a smooth Fano manifold which caries a Kähler Ricci soliton, then the canonical cone of the product of with a complex projective space of sufficiently lar…
The weighted Hermite--Einstein equation
Michael Hallam, Abdellah Lahdili
We introduce a new weighted version of the Hermite--Einstein equation, along with notions of weighted slope (semi/poly)stability, and prove that a vector bundle admits a weighted H…
Weighted cscK metric (I): a priori estimates
Eleonora Di Nezza, Simon Jubert, Abdellah Lahdili
Let be a compact Kähler manifold. In this paper we study the existence of constant weighted scalar curvature Kähler (weighted cscK) metrics on . More precisely, we establish…
Mabuchi Kähler solitons versus extremal Kähler metrics and beyond
Vestislav Apostolov, Abdellah Lahdili, Yasufumi Nitta
Using the Yau-Tian-Donaldson type correspondence for -solitons established by Han-Li, we show that a smooth complex -dimensional Fano variety admits a Mabuchi soliton provide…
The Einstein-Hilbert functional and the Donaldson-Futaki invariant
Abdellah Lahdili, Eveline Legendre, Carlo Scarpa
Given a Kaehler manifold polarised by a holomorphic ample line bundle, we consider the circle bundle associated to the polarisation with the induced transversal holomorphic structu…
Weighted K-stability and coercivity with applications to extremal Kahler and Sasaki metrics
Vestislav Apostolov, Simon Jubert, Abdellah Lahdili
We show that a compact weighted extremal Kahler manifold (as defined by the third named author) has coercive weighted Mabuchi energy with respect to a maximal complex torus in the…
Convexity of the weighted Mabuchi functional and the uniqueness of weighted extremal metrics
Abdellah Lahdili
We prove the uniqueness, up to a pull-back by an element of a suitable subgroup of complex automorphisms, of the weighted extremal Kähler metrics on a compact Kähler manifold intro…
Kähler metrics with constant weighted scalar curvature and weighted K-stability
Abdellah Lahdili
We introduce a notion of a Kähler metric with constant weighted scalar curvature on a compact Kähler manifold , depending on a fixed real torus in the reduced group…
Conformally Kähler, Einstein--Maxwell metrics and boundedness of the modified Mabuchi-functional
Abdellah Lahdili
We prove that if a compact smooth polarized complex manifold admits in the corresponding Hodge Kähler class a conformally Kähler, Einstein--Maxwell metric, or more generally, a Käh…
Automorphisms and deformations of conformally Kähler, Einstein-Maxwell metrics
Abdellah Lahdili
We obtain a structure theorem for the group of holomorphic automorphisms of a conformally Kähler, Einstein-Maxwell metric, extending the classical results of Matsushima, Licherowic…