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RESEARCH INSTERESTS |
I. Harmonic Analysis on Manifolds:
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II. Nonlinear differential equations:
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THESIS |
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PUBLICATIONS |
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Xiangjin Xu, Heat kernel Gaussian bounds on manifolds I: manifolds with non-negative Ricci curvature, arXiv:1912.12758 [math.DG] () Xiangjin Xu, Sharp Hamilton's Gradient and Laplacian Estimates on noncompact manifolds. (Submitted April 2025) () Xiangjin Xu, Heat kernel and Green's function on manifolds with nonnegative Ricci curvature. (Submitted May 2025) () Xing Wang,Xiangjin Xu, Cheng Zhang, $L^p$-Logvinenko-Sereda sets and $L^p$-Carleson measures on compact manifolds. arXiv:2506.22759 [math.AP]. (Submitted July 2025) () Xiangjin Xu, Heat kernel Gaussian bounds on manifolds II: manifolds with negative Ricci curvature, preprint. () Xiangjin Xu, Sharp Hamilton's Gradient and Laplacian Estimates on noncompact manifolds.preprint. () Xiangjin Xu, Differential Harnack inequalities on Riemannian manifolds II: Schr\"odinger operator. (In Progress) () Xiangjin Xu, The Perelman-type entropy formula for linear heat equation on noncompact manifolds. (In Progress) () Xiangjin Xu, New uniqueness criteria of tangent cones for manifolds with nonnegative Ricci curvature. (In Progress) () Xiangjin Xu, Multiple periodic solutions of super-quadratic Hamiltonian systems with bounded forcing terms.(In Progress) () Xiangjin Xu, Periodic and subharmonic solutions of Hamiltonian systems possessing "super-quadratic" potentials. (In Progress) () |
My research is partially supported by: NSF-DMS 0602151(2006 - 2008) and NSF-DMS-0852507 (2008 - 2010),Harpur College Grants in Support of Research, Scholarship and Creative Work: Year 2010-2011, Year 2012-2013, Year 2017-2018, Year 2019-2020. NYS/UUP Individual Development Awards: Year 2013-2014. AMS-NSF Travel grants: ICM 2010 in Hyderabad, India, Augest 2010. PIMS conference, UBC, Canada, July 2013. The Second PRIMA Congress, Shanghai, China, June 2013. MCA 2021 (Online), July, 2021. MCA 2025, Miami, July, 2025. |
Last updated: 07/01/2025