Preprints and Publications (in the order they appeared on arXiv)
- Minimal slopes
and bubbling for complex Hessian equations (with Ramesh Mete
and Jian Song),
arXiv
link.
- Diameter
rigidity for Kähler manifolds with positive bisectional
curvature (with Harish Seshadri), Math. Ann. Volume 385, pages 471–479 (2023),
journal link ,
arXiv
link.
- Kähler-Einstein
metric near an isolated log canonical singularity (with Xin Fu
and Jian Song), to appear in J. Reine Angew. Math. (Crelle's
journal),
journal link (online first)
arXiv
link.
- Metric
rigidity of Kähler manifolds with lower Ricci bounds and almost
maximal volume (with Harish Seshadri and Jian Song), Proc. of
the AMS, 149 (2021), no. 8, 3569–3574
journal link ,
arXiv
link.
- A numerical
criterion for generalised Monge-Ampere equations on projective
manifolds (with Vamsi Pingali), Geom. Func. Anal. (GAFA),
31 (2021), no. 4, 767--814,
journal link,
arXiv
link.
- On coupled
constant scalar curvature Kähler metrics (with Vamsi Pingali),
J. Symplectic Geom., 18 (2020), no. 4, 961–994,
journal link , arXiv
link.
- Adiabatic limits
of anti-self-dual connections on collapsed K3 surfaces (with
Adam Jacob and Yuguang Zhang), J. Differential Geom., 118 (2021)
223-296.
journal link , arXiv
link.
- Hermitian-Yang-Mills connections on collapsing elliptically
fibered K3 surfaces (with Adam Jacob),
J. Geom. Anal., 32, Article - 69 (online only),
journal link, arXiv
link.
- Expansions of solutions to extremal metric type equations on
blow-ups of cscK surfaces, Ann. Global Anal. Geom., 55 (2019),
no. 2, 215–241,
journal link , arXiv
link.
- Kähler-Einstein metrics along the smooth continuity method
(with Gábor Székelyhidi), Geom. Funct. Anal. (GAFA),
26 (2016),
no. 4, 975--1010,
journal link, arXiv
link.
- On convexity of the regular set of conical Kähler-Einstein
metrics, Math. Res. Lett., 23 (2016), no. 1, 105--126,
journal link, arXiv
link.
- A remark on
Kähler metrics with conical singularities along a simple normal
crossing divisor (with Jian Song), Bull. Lond. Math. Soc., 47
(2015), no. 6, 1010--1013,
journal link, arXiv
link.
- Connecting toric manifolds by conical Kähler-Einstein metrics
(with Bin Guo, Jian Song and Xiaowei Wang), Advances in Math., 323
(2018), 38-83,
journal link, arXiv
link.
Surveys and expository articles
Comparison and
Rigidity Theorems for the Volume and Diameter of Positively Curved
Kähler Manifolds (with Harish Seshadri), Acta Mathematica Sinica, English Series
Published online: December 13, 2024 https://doi.org/10.1007/s10114-024-3479-1
journal link
An overview
of the work of Karen Uhlenbeck (with Agnid Banerjee), The Mathematics Consortium Bulletin July 2020 Vol. 2, Issue 1
journal link
Videos of some select talks
Minimal slopes and singular
solutions for complex Hessian equation INI, Cambridge, UK,
May 2024.
Moment maps and canonical metrics in
complex geometry Virtual Math Fest
July 2020.
Slides of some select talks
Kahler-Einstein metrics along the smooth
continuity methods IISc, January, 2018.
(Inverse) Hessian equations and positivity
conditions in Kahler geometry CMI alumini talks (webinar), June, 2020.
Notes
AIS IISc July, 2019 -
Lecture notes on Calabi's conjectures and
Kahler-Einstein metrics