个人简介
一直从事整体微分几何与几何分析研究，相关成果发表在《J. Differential Geom.》、《Geom. Funct. Anal.》、《Math. Ann.》、《Math. Res. Lett.》、《Comm. Anal. Geom.》、《Proc. Amer. Math. Soc.》、《Science China Math.》、《Chin. Ann. Math. Ser. B》等国内外刊物。先后主持承担国家自然科学基金面上项目和青年项目各一项、中国博士后科学基金特别资助项目和面上项目各一项。
教学与课程
主要承担本科生的《线性代数》、《解析几何》、《微分几何》和研究生的《微分流形》等课程。
育人成果
科研项目
科研成果
1. H. W. Xu, L. Lei, J. R. Gu , Generalized Ejiri's rigidity theorem for submanifolds in pinched manifolds, Chin. Ann. Math., Ser. B, 2020, 41(2): 285-302. 2. J.R. Gu, H. W. Xu, The topological sphere theorem for odd-dimensional compact submanifolds with pinched Ricci curvature Proceedings of the 7th International Congress of Chinese Mathematicians, Vol.II, ALM 44, HEP/IP, 2019, pp. 253-268.3. J.R.Gu and H.W.Xu, A sharp differentiable pinching theorem for submanifolds in space forms, Proc. Amer. Math. Soc., 144(2016), 337-346.4. H.W.Xu, L.Lei and J.R.Gu, On Yau rigidity theorem for submanifolds in pinched manifolds, Pure Appl. Math. Q., 12(2016), 301-303.5. J.R.Gu, Y.Leng and H.W.Xu, Rigidity of closed submanifolds in a locally symmetric Riemannian manifold, Appl. Math. J. Chinese Univ. Ser.B, 31(2016), 237-252. 6. J.R.Gu,H.W.Xu, Z.Y.Xu and E.T.Zhao, A survey on rigidity problems in geometry and topology of submanifolds, Proceedings of the 6th International Congress of Chinese Mathematicians, Vol.II, ALM 37, HEP/IP, 2016, pp. 79-99 7. H.W.Xu and J.R.Gu, Rigidity of Einstein manifolds with positive scalar curvature, Math. Ann., 358(2014), 169-193.8. H.W. Xu, Y. Leng and J.R.Gu, Geometric and topological rigidity for compact submanifolds of odd dimension, Sci. China Math., 57(2014), 1525-1538. 9. H.W.Xu and J.R.Gu, Geometric, topological and differentiable rigidity of submanifolds in space froms, Geom. Funct. Anal., 23(2013), 1684-1703. 10. J.R. Gu and H.W. Xu, The sphere theorems for manifolds with positive scalar curvature, J. Differential Geom., 92(2012), 507-545.11 J.R.Gu and H.W.Xu, On Yau rigidity theorem for minimal submanifolds in spheres, Math. Res. Lett., 19(2012), 511-523.12. H.W.Xu and J.R.Gu, The differentiable sphere theorem for manifolds with positive Ricci curvature, Proc. Amer. Math. Soc., 140(2012), 1011-1021.13. H.W.Xu, F. Huang, J.R.Gu and M.Y.He, Ln/2 pinching theorem for submanifolds with parallel mean curvature in Hn+p(-1), Pure Appl. Math. Q., 8(2012), 1097- 1116.14. H.W.Xu and J.R.Gu, An optimal differentiable sphere theorem for complete manifolds, Math. Res. Lett., 17(2010), 1111-1124. 15. H.W.Xu and J.R.Gu, A general gap theorem for submanifolds with parallel mean curvature in Rn+p, Comm. Anal. Geom., 15(2007), 175-194. 16. H.W.Xu and J.R.Gu, L2-isolation phenomenon for complete surfaces arising from Yang-Mills theory, Lett. Math. Phys., 80(2007), 115-126.
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