Publications and Preprints:
- Degenerating hyperbolic surfaces and spectral gaps for large genus. Joint with Yunhui Wu and Haohao Zhang.
arXiv:2201.03056. Accepted by Analysis and PDE. - Spherical conical metrics and harmonic maps to spheres. Joint with Mikhail Karphukhin.
Transactions of the AMS, Volume 375, Number 5, May 2022, Pages 3325–3350. Journal version - Fundamental gaps of spherical triangles. Joint with Shoo Seto and Guofang Wei.
Annals of Global Analysis and Geometry 61, pages1–19 (2022). Journal version - Spectral properties of reducible conical metrics. Joint with Bin Xu.
Illinois Journal of Mathematics, Vol. 65, No. 2 (2021), 313–337. Journal version - Conical metrics on Riemann surfaces, II: spherical metrics. Joint with Rafe Mazzeo.
International Mathematics Research Notices, Volume 2022, Issue 12, June 2022, Pages 9044–9113. Journal version - Rigidity of a family of spherical conical metrics.
New York Journal of Mathematics 26 (2020) 272–284. Journal version - Spherical conic metrics and realizability of branched covers.
Proceedings of the AMS, Volume 147, Number 4, April 2019, Pages 1805–1815. Journal version - Conical metrics on Riemann surfaces, I: the compactified configuration space and regularity. Joint with Rafe Mazzeo.
Geometry and Topology 24 (2020) 309–372. Journal version - Boundary behaviour of Weil-Petersson and fiber metrics for Riemann moduli spaces. Joint with Richard Melrose.
International Mathematics Research Notices, Volume 2019, Issue 16, Pages 5012–5065. Journal version - Eleven dimension supergravity equations on edge manifolds.
Annales Henri Poincaré, Volume 19, Issue 8 (2018), 2347–2400. Journal version - Eigenvalue resolution of self-adjoint matrices.
Pacific Journal of Mathematics, Vol. 288 (2017), No. 1, 241–255. Journal version - Resolution of the canonical fiber metrics for a Lefschetz fibration. Joint with Richard Melrose.
Journal of Differential Geometry, Volume 108, Number 2 (2018), 295-317. Journal version - The eleven dimensional supergravity equations, resolutions and Lefschetz fiber metrics. PhD thesis
Talk Slides and Videos:
- Deformation of constant curvature conical metrics
A video of my talk at MSRI, - Spectral properties of reducible conical metrics
A video of my talk at “Spectral geometry in the clouds”. - The compactified configuration space and regularity for conical metrics
- Nodal degeneration of hyperbolic metrics and application to Weil-Petersson metric on the moduli space.
A video of my talk at BIRS/CMO. Another video of my talk at MSRI. - The resolution of canonical fiber metrics for a Lefschetz fibration.
A video of my talk at BIRS. - The eleven dimensional supergravity equations