Interests & Publications
Interests & Publications
My research interests lie in complex differential geometry and geometric analysis.
Examples of topics include:
Existence of canonical metrics on complex manifolds.
Stability of complex manifolds with large symmetry group
As a recent direction, I also study:
The generalization of the above notions to singular varieties.
Formation of singularities along Kahler--Ricci flow.
Canonical metrics on non-Kahler manifold (specially almost-Kahler & Sasakian manifolds).
Publication and pre-print
The list of my pre-print is here
9) Extremal Sasaki manifolds and weighted K-stability, arXiv:2610.10216 (2026), (with Chung-Ming Pan)
8) New extremal Kähler metrics on projective bundles, (2026) arXiv:2609.01094 .
7) Relative uniform Yau--Tian--Donaldson correspondence for projective bundles over a curve (2026), arXiv:2602.13133 (with Chenxi Yin).
6) Numerical invariants for weighted cscK metrics, arXiv:2503.01680 (2025), (with Thibaut Delcroix).
The list of my publications is here
5) Weighted cscK metric (II): the continuity method , (with Eleonora Di Nezza and Abdellah Lahdili), Journal für die reine und angewandte Mathematik (Crelle’s Journal) 832 (2026), 255–296.
4) Weighted cscK metric (I): a priori estimates, Journal of Functional Analysis, 289 (11) 2025 (with Eleonora Di Nezza and Abdellah Lahdili).
3) An effective weighted K-stability condition for polytopes and semisimple principal toric fibrations, Annales Henri Lesbegue, 6 (2023) 117-149. (with Thibaut Delcroix).
2) A Yau--Tian--Donaldson correspondence on a class of toric fibrations, Annales de l'Institut Fourier, 73 (2023) no. 6, pp. 2567-2604.
1) Weighted K-stability and coercivity with applications to extremal Kähler and Sasaki metrics, Geometry & Topology, 27 (2023) 8, 3229-3302 (with Vestislav Apostolov and Abdellah Lahdili).
Some keywords: canonical metrics, variational approach, moment map and moment polytope, Lie groups and Lie algebras, hamiltonian action, principal bundle, fibrations, toric manifolds, K-stability, Kähler–Ricci flow.