许明，男，首都师范大学数学科学学院副教授，硕士生导师。博士毕业于美国纽约州立大学石溪分校，研究方向为几何学。2016年以来，研究齐性几何与芬斯勒几何，在芬斯勒几何中的CW-变换与CW-齐性、齐性正曲率空间分类、闭测地线、等参超曲面等课题研究中取得成果，在《J. Diff. Geom.》、《J. Geom. Anal.》、《Ann. Mat. Pura Appl.》、《Transform. Groups》等期刊上发表了37篇论文。目前主持国家自科面上、北京自科面上，参与国家自科创新群体、北京自科重点专项等项目。

1. M. Xu, Submersion and homogeneous spray geometry, J. Geom. Anal, accepted, arXiv:2111.10558.
2. M. Xu, Left invariant spray structure on a Lie group, J. Lie Theory, accepted, arXiv:2103.08901.
3. M. Xu and J. Tan, Isoparametric hypersurfaces induced by navigation in Lorentz Finsler geometry, Acta. Math. Sci., accepted, arXiv:2105.08900.
4. L. Zhang and M. Xu, Standard homogeneous (α1, α2 )-metrics and geodesic orbit property, Math. N., accepted, arXiv:1912.00210.
5. M. Xu, The Minkowski norm and Hessian isometry induced by an isoparametric foliation on the unit sphere, Sci. China Math. (2021), accepted, doi:10.1007/s11425-020-1871-9.
6. M. Xu and V.S. Matveev, Proof of Laugwitz conjecture and Landsberg unicorn conjecture for Minkowski norms with SO(k)×SO(n-k)-symmetry, Canad. J. Math (2021), accepted, doi: 10.4153/S0008414X21000304.
7. M. Xu and Yu.G. Nikonorov, Algebraic properties of bounded Killing vector fields, Asian J. Math. (2021), accepted.
8. M. Xu, Geodesic orbit Finsler space with K≥0 and the (FP) condition, Adv. Geom. (2021), accepted, doi:10.1515/advgeom-2021-0023.
9. M. Xu and S. Deng, The Landsberg equation of a Finsler space, Ann. Sc. Norm. Super. Pisa Cl. Sci. (5) 12 (2021), 31-51.
10. M. Xu, Homogeneous Finsler spaces with only one orbit of prime closed geodesics, Sci. China Math. 63 (11) (2020), 2321-2342.
11. M. Xu, V.S. Matveev, Ke Yan and S. Zhang, Some geometric correspondences for homothetic navigation, Publ. Math. Debrecen 97 (3-4) (2020), 449-474.
12. M. Xu and J. Li, Willmore orbits for isometric Lie actions, Math. Z. 292 (3-4) (2019), 1479-1493.
13. M. Xu, Finsler spheres with constant flag curvature and finite orbits of prime closed geodesics, Pacific J. Math. 302 (1) (2019), 353-370.
14. M. Xu and S. Deng, Geodesic and curvature of piecewise flat Finsler surfaces, J. Geom. Anal. 28 (2) (2018), 1341-1372.
15. M. Xu, Isoparametric hypersurfaces in a Randers sphere of constant flag curvature, Ann. Mat. Pura Appl. (4) 197 (3) (2018), 703-720.
16. M. Xu and S. Deng, Towards the classification of odd dimensional homogeneous reversible Finsler spaces with positive flag curvature, Ann. Mat. Pura Appl. (4) 196 (4) (2017), 1459-1488.
17. M. Xu and S. Deng, Homogeneous Finsler spaces and the flag-wise positively curved condition, Forum Math. 30 (6) (2018), 1521-1537.
18. M. Xu, Geodesic orbit spheres and constant curvature in Finsler geometry, Diff. Geom. Appl. 61 (2018), 197-206.
19. M. Xu and L. Zhang, δ-Homogeneity in Finsler geometry and the positive curvature problem, Osaka J. Math. 55 (1) (2018), 177-194.
20. J.A. Wolf, F. Podesta and M. Xu, Toward a classification of Killing vector fields of constant length on pseudo-Riemannian normal homogeneous spaces, J. Diff. Geom. 105 (3) (2017), 519-532.
21. M. Xu, S. Deng, L. Huang and Z. Hu, Even dimensional homogeneous Finsler spaces with positive flag curvature, Indiana Univ. Math. J. 66 (3) (2017), 949-972.
22. M. Xu and S. Deng, Normal homogeneous Finsler spaces, Transform. Groups 22 (4) (2017), 1143-1183.
23. M. Xu and W. Ziller, Reversible homogeneous Finsler metrics with positive flag curvature, Forum Math. 29 (5) (2017), 1212-1226.
24. M. Xu, Examples of flag-wise positively curved spaces, Diff. Geom. Appl. 52 (2017), 42-50.
25. M. Xu and S. Deng, Rigidity of negatively curved geodesic orbit Finsler spaces, C. R. Math. 355 (9) (2017), 987-990.
26. S. Deng and M. Xu, (α_1,α_2 )-metrics and Clifford-Wolf homogeneity, J. Geom. Anal. 26 (3) (2016), 2282-2321.
27. M. Xu and J.A. Wolf, Killing vector fields of constant length on Riemannian normal homogeneous spaces, Transform. Groups 21 (3) (2016), 871-902.
28. M. Xu and S. Deng, Homogeneous (α,β)-spaces with positive flag curvature and vanishing S-curvature, Nonlinear Anal. 127 (2015), 45-54.
29. M. Xu and S. Deng, Clifford-Wolf homogeneous Finsler metrics on spheres, Ann. Mat. Pura Appl. (4) 194 (3) (2015), 759-766.
30. S. Deng and M. Xu, Left invariant Clifford-Wolf homogeneous (α,β)-metrics on compact semisimple Lie groups, Transform. Groups 20 (2) (2015), 395-416.
31. M. Xu and J.A. Wolf, Sp(2)\/U(1) and a positive curvature problem, Diff. Geom. Appl. 42 (2015), 115-124.
32. M. Xu and S. Deng, Killing frames and S-curvature of homogeneous Finsler spaces, Glasg. Math. J. 57 (2) (2015), 457-464.
33. S. Deng and M. Xu, Clifford-Wolf translations of homogeneous Randers spheres, Israel J. Math. 199 (2) (2014), 507-725.
34. S. Deng and M. Xu, Clifford-Wolf translations of Finsler spaces, Forum Math. 26 (5) (2014), 1413-1428.
35. S. Deng and M. Xu, Clifford-Wolf translations of left invariant Randers metrics on compact Lie groups, Quart. J. Math 65 (1) (2014), 133-148.
36. M. Xu and S. Deng, Clifford-Wolf Homogeneous Randers Spaces, J. Lie Theory 23 (3) (2013), 837-845.
37. N.C. Leung and M. Xu, Compactness of the massive Seiberg-Witten equation, Asian J. Math. 13 (3) (2009), 359-367.

讲授课程：
1. 拓扑学1（本科生专业选修课）；2. 李群李代数（研究生基础课）

指导硕士研究生：
1. 胡娜；2. 梁美娟；3. 曲春霖；4. 徐熙昀；5. 张佳林

本领域重要国内/国际学术会议和所作报告
[1] 2016.05，天津，黎曼芬斯勒几何及相关课题会议，国际会议，The study on Clifford-Wolf translations, Clifford-Wolf homogeneity, and Killing vector field of constant length
[2] 2017.06，天津，表示论与调和分析国际会议，国际会议，Lie method in the study of Willmore functional and Willmore submanifold
[3] 2017.07，乌鲁木齐，黎曼芬斯勒几何及相关课题会议，国际会议，Classification of positively curved homogeneous Finsler spaces and related topics，
[4] 2018.05，意大利比萨，国际芬斯勒几何研讨会，国际会议，Homogeneous Finsler spaces with positive flag curvature, classification and related topics
[5] 2018.07，厦门，黎曼芬斯勒几何及相关课题会议，国内会议，Geodesic and curvature of piecewise flat Finsler surfaces
[6] 2019.06，莆田，黎曼芬斯勒几何及相关课题会议，国内会议，Lie method in the study of closed geodesics on Finsler spheres with constant curvature and compact homogeneous Finsler spaces
[7] 2019.08，伊朗德黑兰，对称空间与芬斯勒几何暑期班与研讨会，国际会议，Series talks on homogeneous Finsler geometry
[8] 2019.11，成都，第三届泛太平洋拓扑与几何会议，国际会议，Geometric correspondences of homothetic navigation
[9] 2021.1，日本，第55届芬斯勒几何研讨会，线上国际会议，Laugwitz Conjecture, Landsberg Conjectures, Minkowski norm and Hessian isometry induced by an isoparametric foliation on a unit sphere
[10] 2021.7，哈尔滨，第17届全国李理论会议，Some algebraic properties of bounded Killing vector fields

2015年2月，“李群与黎曼-芬斯勒几何”，高校优秀科研成果奖（自然科学奖），第四完成人

Since 2016, I have studied homogeneous geometry and Finsler geometry, made progress on the research projects of CW-translation and CW-homogeneity, classification of homogeneous positive curvature, closed geodesic, isoparametric hypersurfaces in Finsler geometry, and published 37 papers on J. Diff. Geom., Sci. China Math., Math. Z., J. Geom. Anal., Canad. J. Math., Ann. Mat. Pura Appl., Transform. Groups, etc. Right now, I have directed general projects of NSF China and Beijing, and participated major projects of NSF China and Beijing respectively.