Publications

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Comparison and rigidity theorems for the volume and diameter of positively curved Kahler manifolds

(with Ved Datar) To appear in Acta Mathematica Sinica. pdf

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Diameter rigidity for Kahler manifolds with positive bisectional curvature

(with Ved Datar) Math. Ann. 183 (2022). pdf

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Metric rigidity of Kahler manifolds with lower ricci bounds and almost maximal volume

(with Ved Datar and Jian Song) Proceedings of the AMS 149 (2021), 3569-3574. pdf

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On domains biholomorphic to Teichmuller space

(with Subhojoy Gupta) IMRN 2020 (2020), 2542-2560. pdf

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A gap theorem for positive Einstein metrics on 4-sphere

(with Kazuo Akutagawa, Hisaaki Endo), Math. Ann. 373 (2019), 1329-1339. pdf

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Holomorphic motions and complex geometry

(with Herve Gaussier), Proceedings of the AMS 147 (2019), 185-197. pdf

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On the Gromov hyperbolicity of convex domains in C^n

(with Herve Gaussier), Computional Methods and Function Theory 18 (2018), 617-641. pdf

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Quot schemes and Ricci semipositivity

(with Indranil Biswas) C. R. Acad. Sci. Paris Ser. I Math. 355 (2017), 577-581. pdf

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Chern scalar curvature and symmetric products of Riemann surfaces

(with Indranil Biswas), Pure and Appld. Math. Quart. 12 (2016), 463-471. pdf

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Positive isotropic curvature and self-duality in dimension 4,

(with Thomas Richard) Manuscripta Mathematica 149 (2016), 443-457. pdf

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A gap theorem for Ricci-flat 4 manifolds

(with Atreyee Bhattacharya) Differential Geometry and its Applications 40 (2015), 269-277. pdf

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Non-coercive Ricci flow invariant curvature cones

(with Thomas Richard), Proceedings of AMS 143 (2015), 2661-2674. pdf

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On the Kahler structures over quot schemes II,

(with Indranil Biswas), Illinois Journal of Mathematics 58 (2014), 689-694. pdf

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On the Kahler structures over quot schemes

(with Indranil Biswas), Illinois Journal of Mathematics 57 (2013), 1019-1024. pdf

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On Wilking's criterion for the Ricci flow

(with H. A. Gururaja and Soma Maity), Mathematische Zeitschrift 274 (2013), 471-481. pdf

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Totally geodesic discs in strongly convex domains

(with Herve Gaussier), Mathematische Zeitschrift 274 (2013), 185-197. pdf

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3-manifold groups, Kahler groups and complex surfaces

(with Indranil Biswas and Mahan Mj), Communications in Contemporary Mathematics 14 (2012) pdf

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Almost quarter-pinched Kahler metrics and Chern numbers

(with Martin Deraux), Proceedings of the AMS 139 (2011), 2571-2576. pdf

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Surfaces of bounded mean curvature in Riemannian manifolds

(with Siddartha Gadgil), Transactions of the AMS 363 (2011), 3977-4005. pdf

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Almost-Einstein manifolds with nonnegative isotropic curvature,

Annales de l'institut Fourier 60 (2010), 2493-2501. pdf

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Manifolds with nonnegative isotropic curvature,

Communications in Analysis and Geometry 17 (2009), 621-635. pdf

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On the topology of manifolds with positive isotropic curvature

(with Siddartha Gadgil), Proceedings of the AMS 137 (2009), 1807-1811. pdf

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An elementary approach to gap theorems,

Proceedings of the Indian Academy of Sciences 119 (2009), 197-?201. pdf

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On the compactness of isometry groups in complex analysis,

(with Kaushal Verma), Complex Variables and Elliptic Equtions 54 (2009), 387-399. pdf

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Complex product manifolds cannot be negatively curved,

(with Fangyang Zheng), Asian Journal of Mathematics 12 (2008), 145-149. pdf

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Domains in complex surfaces with non-compact automorphism groups,

(with Kaushal Verma), Journal of Mathematical Analysis and Applications 337 (2008), 1273-1283. pdf

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On isometries of the Kobayashi and Caratheodory metrics of strongly pseudoconvex domains,

(with Kaushal Verma), Annali della Scuola Normale Superiore di Pisa (5) 5 (2006), no. 3, 393-417. pdf

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Negative sectional curvature and the product complex structure,

Mathematical Research Letters, 13 (2006), no. 3, 495-500. pdf

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A class of nonpositively curved Kahler manifolds biholomorphic to the unit ball in C^n

(with Kaushal Verma), C. R. Acad. Sci. Paris Ser. I Math, 342 (2006), no. 6, 427-430 pdf

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Weyl curvature and the Euler characteristic in dimension four,

Differential Geometry and its Applications, 24 (2006), no. 2, 172-177. ps

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Positive scalar curvature and minimal hypersurfaces,

Proceedings of the American Mathematical Society, 133 (2005), 1497-1504. ps

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Einstein 4-manifolds with S^1-actions,

Mathematische Zeitschrift, 247 (2004),no. 3, 487-503. pdf

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A note on negative isotropic curvature,

Mathematical Research Letters, 11 (2004), no. 2-3, 365-370. pdf

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The Weyl functional near the Yamabe invariant

(with K. Akutagawa, B. Botvinnik and O. Kobayashi),

 Journal of Geometric Analysis, 13 (2003), no. 1, 1-20 ps

Automated music

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An algorithmic approach to South Indian classical music

(with Shayan Garani), Journal of Mathematics and Music 13 (2019), 107-134. pdf

Surveys and expository articles

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Some spects of the automorphisms groups of domains

(with Kaushal Verma), to appear in the Handbook of Group Actions, Volume IV, International Press. pdf

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Ricci flow and the Poincare conjecture (with Siddartha Gadgil). pdf

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Pune AIS Notes. pdf

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Mumbai ATM Notes. pdf