Publication List

ZHONGMIN SHEN

Updated on August 31, 2008

 

a.   Articles in Refereed Journals

 

1.    Z. Shen, The first eigenvalue of an irreducible homogeneous manifold, Chinese Ann. Math. Ser. B 9(1988), no. 3, 270-273. Math. Review 90b:58272

2.   Z. Shen, A sphere theorem for manifolds of positive Ricci curvature, Indiana University Mathematics Journal, 38 (1989), no.1, 229-233. Math. Review 90h:53044

3.   Z. Shen, Finiteness and vanishing theorems for complete Riemannian manifolds, Bulletin of the American Mathematical Society, 21 (1989), no.2, 241-244. Math. Review 90c:53111

4.   Z. Shen, Some rigidity phenomena for Einstein metrics, Proceedings of the American Mathematical Society, 108 (1990), no.4, 981-987. Math. Review 90g:53059

5.   Z. Shen and G. Wei, On Riemannian manifolds with almost nonnegative curvature, Indiana University Mathematics Journal, 40 (1991), no.2, 551-565. Math. Review 92e:53053

6.   Z. Shen, On Riemannian manifolds with e-maximal diameter and bounded curvature, Mathematische Zeitschrift, 201 (1992), no.3, 465-473. Math. Review 93h:53037

7.   Z. Shen, Rigidity theorems for nonpositive Einstein metrics, Proceedings of the American Mathematical Society, 116 (1992), no.4,  1107-1114. Math. Review 93b:53041

8.   Z. Shen, On complete manifolds of nonpositive kth-Ricci curvature, Transactions of American Mathematical Society, 338 (1993), no.1, 289-310. Math. Review 93j:53054

9.   Z. Shen and G. Wei,Volume growth and finite topological type, Differential Geometry: Riemannian geometry (Los Angeles, CA, 1990), 539-549, Proceedings of Symposia in Pure Mathematics, 54, Part 3,  Amer. Math. Soc., Providence, RI, 1993. Math. Review 94e:53036

10. Z. Shen, A regularity theorem for Alexandrov spaces, Math. Nachr. 164(1993), 91-102. Math. Review 94j:53054

11. P.Petersen, Z.Shen and S.Zhu, Manifolds with small excess and bounded curvature, Mathematische Zeitschrift, 212 (1993), no.4, 581-585. Math. Review 94c:53052

12. Z. Shen, On complete Riemannian manifolds with collapsed ends, Pacific Journal of Mathematics, 163 (1994),  no.1, 175-182. Math. Review 94m:53049

13. Z. Shen, Deforming metrics with curvature and injectivity radius bounded from below, Archiv der Mathematik, 62 (1994), no.4, 354-367. Math. Review 95a:53056

14. Z. Liu and Z. Shen, On the Betti numbers of Alexandrov spaces, Annals of Global Analysis and Geometry, 12 (1994), no.2, 123-133. Math. Review 95b:53055

15. X. Dai, Z. Shen and G. Wei, Negative Ricci curvature and isometry group, Duke Journal of Mathematics, 76 (1994),  no.1, 59-73. Math. Review 96e:53051

16. Z. Shen, On a connection in Finsler geometry, Houston Journal of Mathematics, 20 (1994), no.4, 591-602. Math. Review 95i:53021

17. D. Bao and Z. Shen, On the volume of unit tangent spheres in a Finsler manifold, Results in Mathematics, 26 (1994), no.1-2, 1-17. Math. Review 95h:53096

18. Z. Shen, A convergence theorem for Riemannian submanifolds, Transactions of the American Mathematical Society, 347 (1995), no.4, 1343-1350. Math. Review 95g:53045

19. Z. Shen, Some formulas of Gauss-Bonnet-Chern type in Riemann-Finsler geometry, Journal fur die reine und angewandte Mathematik, 475 (1996), 149-165. Math. Review 97h:53074

20. Z. Shen, Finsler manifolds of constant curvature, Finsler geometry (Seattle, WA, 1995), 83-93, Contemporary Mathematics, 196, Amer. Math. Soc., Providence, RI, 1996. Math. Review 97m:53120

21. D. Bao, S.S. Chern and Z. Shen, On the Gauss-Bonnet integrand for 4-dimensional Landsberg spaces, Finsler geometry (Seattle, WA, 1995), 15-26, Contemporary Mathematics, 196, Amer. Math. Soc., Providence, RI, 1996. Math. Review 97g:53085

22. Z. Shen, Complete manifolds with nonnegative Ricci curvature and large volume growth, Inventiones mathematicae, 125 (1996), 393-404. Math. Review 97d:53045

23. Z. Shen, Volume comparison and its applications in Riemann-Finsler geometry, Advances in Mathematics 128 (1997), no. 2, 306-328. Math. Review 98j:53081

24. D. Bao, S.S. Chern and Z. Shen, Rigidity of Finsler structures on surfaces, Collection of papers in honour of Academician Radu Miron on his 70th birthday, Revue Roumaine de Mathematiques Pures et Appliquees, 42(1997), no. 9-10, 707-735. Math. Review 99h:53099

25. J. Sha and Z. Shen, Complete manifolds with nonnegative Ricci curvature and quadratically nonnegative curved infinity, American Journal of Mathematics, 119(1997), no.6, 1399-1404. Math. Review 99a:53046

26. Z. Liu, Z. Shen and D. Yang, Riemannian manifolds with conical singularities, Rocky Mountain Journal of Mathematics, 28(1998), no.2, 625-641. Math. Review 2000a:53058

27. Z. Liu and Z. Shen, Riemannian geometry of conical singular sets, Annals of Global Analysis and Geometry, 16(1998), no.1, 29-62. Math. Review 99e:53054

28. Z. Shen, The non-linear Laplacian for Finsler manifolds, The theory of Finslerian Laplacians and applications, 187-198, Math. Appl., 459, Kluwer Acad. Publ., Dordrecht, 1998. Math. Review 2000a:58060

29. Z. Shen, On Finsler geometry of submanifolds, Mathematische Annalen, 311(1998), no. 3, 549-576. Math. Review 99j:53095

30. W. Gu and Z. Shen, Levy concentration of metric measure manifolds, Finslerian geometries (Edmonton, AB, 1998), 169-177, Fundamental Theories of Physics, 109, Kluwer Acad. Publ., Dordrecht, 2000. Math. Review 2003b:53042

31. J. Lott and Z. Shen, Manifolds with quadratic curvature decay and slow volume growth, Annales Scientifiques de l’Ecole Normale Superieure, 33 (2000), 275-290. Math. Review 2002e:53049

32. Z. Shen, A rigidity theorem for Finsler submanifolds, Proceedings of the 11th National Conference on Finsler, Lagrange and Hamilton Geometry (Craicova, 2000), Algebras Groups Geom. 17(2000),  no. 3, 341-350. Math. Review 2002b:53061

33. Y. Ge and Z. Shen, Eigenvalues and eigenfunctions of Finsler mm manifolds, Proceeding of the London Mathematical Society, 82(2001), 725-746. Math. Review 2002g:58059

34. Z. Shen, On R-quadratic Finsler spaces, Publications Mathematicae, Debrecen. 58 (2001), no. 1-2,  263-274. Math. Review 2001j:53034

35. Z. Shen and C. Sormani, The codimension one homology of a complete manifold with nonnegative Ricci curvature, American Journal of Mathematics, 123(2001), 515-524. Math. Review 2002i:53048

36. Z. Shen, On projectively related Einstein metrics in Riemann-Finsler geometry, Mathematische Annalen, 320 (2001), 625-647. Math. Review 2002f:53075

37. Z. Shen, Conjugate radius and positive scalar curvature, Mathematische Zeitschrift, 238(2001), 431-439. Math. Review 2002k:53066

38. X. Mo and Z. Shen, Recent developments and some open problems in Finsler geometry, Chinese Sci. Bull. 46(2001), 1059-1061. Math. Review 2002i:53032

39. Z. Shen, Geometric meanings of curvatures in Finsler geometry, Proceedings of the 20th Winter School “Geometry and Physics” (Srni, 2000). Rend. Circ. Mat. Palermo (2) Suppl. No. 66 (2001), 165-178. Math Review 2002e: 53029

40.  H. Zhan and Z. Shen, The volume and topology of a complete Riemannian manifold, Chinese Ann. Math. Ser. B 22(2001), 85-92.  Math. Review 2002c:53056

41. M. Ji and Z. Shen, On strongly convex graphs in Minkowski geometry, Canadian Mathematical Bulletin, 45(2) (2002), 232-246.

42. D. Bao and Z. Shen, Finsler metrics of constant curvature on the Lie group S^3,Journal of the London Mathematical Society, 66(2002), 453-467.

43. Z. Shen, Two-dimensional Finsler metrics of constant curvature, Manuscripta Mathematica, 109(3)(2002), 349-366.

44. Z. Shen, Projectively flat Randers metrics of constant curvature, Mathematische Annalen, 325(2003), 19-30.

45. Z. Shen, Projectively flat Finsler metrics of constant flag curvature, Transactions of the American Mathematical Society, 355(4)(2003), 1713-1728.

46. Z. Shen, Finsler metrics with K=0 and S=0, Canadian Journal of Mathematics, 55(2003), no.1, 112-132.

47. X. Chen and Z. Shen, A comparison theorem on the Ricci curvature in projective geometry, Annals of Global Analysis and Geometry, 23(2003), 141-156.

48. X. Chen and Z. Shen, Randers metrics with special curvature properties, Osaka Journal of Mathematics, 40(2003), 87-101.

49. X. Chen, X. Mo and Z. Shen, On the flag curvature of Finsler metrics of scalar curvature, Journal of the London Mathematical Society, (2) 68 (2003), 762-780.

50. D. Bao, C. Robles and Z. Shen, Zermelo navigation on Riemannian manifolds, Journal of Differential Geometry, 66(2004), 391-449. MR:2106471(2005k:58023).

51. X. Chen and Z. Shen, Finsler metrics with special curvature properties. Period. Math. Hungar. 48(2004), no. 1-2,33-47. MR2077684(2005e:53021).

52. Z. Shen, Finsler manifolds with nonpositive flag curvature and constant S-curvature, Mathematische Zeitschrift, 249(2005), 625-639. MR2121744 (2005m:53142)

53. X. Chen and Z. Shen, On Douglas metrics, Publ. Math. Debrecen, 66(3-4)(2005), 503-512. MR2137785 (2005m:53027).

54. X. Mo and Z. Shen, On negatively curved Finsler manifolds of scalar curvature, Canadian Mathematical Bulletin, 48(2005), 112-120. MR: 2118768 (2005k:53128).

55. Z. Shen, Riemann-Finsler geometry with applications to information geometry, Chinese Ann. of Math. Ser. B 27 (2006), no. 1, 73-94. MR2209953

56. Z. Shen and J.-Y. Wu, Ricci curvature, diameter and bounded Betti numbers, Chinese Annals of Mathematics, Series B, 27 (2006), 143-152.

57. X. Chen and Z. Shen, Projectively flat Finsler metrics with almost isotropic S-curvature, Acta Mathematica Scientia, Ser. B Engl. Ed. 26(2006), no. 2, 307-313. MR2219382. 

58. X. Mo, Z. Shen and C. Yang, Some constructions of projectively flat metrics, Science in China, Series A,  49(2006), 703-714.

59. B. Li and Z. Shen, On a class of weakly Landsberg metrics, Science in China, Series A, 50(2007), 75-85.

60. B. Li and Z. Shen, On a class of projectively flat Finsler metrics with constant flag curvature,  International Journal of Mathematics,  Vol. 18, No. 7 (2007), 1-12.

61. B. Najafi, Z. Shen and A. Tayebi, Finsler metrics of scalar flag curvature with special non-Riemannian curvature properties, Geometriae Dedicata, 131(2008), 87-97.

62. Z. Shen and H. Xing, On Randers metrics of isotropic S-curvature, Acta Mathematica Sinica, English Series, 24(2008), 789-796.

63.  Z. Shen and G. C. Yildirim,  On a class of projectively flat metrics with constant flag curvature, Canadian Journal of Mathematics, 60(2008), no. 2, 443-456.

 

 

 

b.     Articles Accepted for Publication

 

64. B. Najafi, Z. Shen and A. Tayebi,  On a projective class of Finsler metrics, Publ. Math.  Debrecen,  accepted.

65.  X. Cheng and Z. Shen, A class of Finsler metrics with isotropic S-curvature,  Israel Journal of Mathematics, accepted

66. Z. Shen, On projectively flat (α,β)-metrics, Canadian Mathematical Bulletin, accepted.

67.  Z. Shen, On a class of Landsberg metrics in Finsler Geometry, Canadian Journal of Mathematics, accepted.

68. B. Li and Z. Shen, Randers metrics of quadratic Riemann curvature, International Journal of Mathematics, accepted.

69. B. Li, Y.B. Shen and Z. Shen, On a class of Douglas metrics in Finsler geometry, submitted to Studia Sci. Math. Hungarica, accepted, 2008.

 

c.      Articles Submitted for Publications

 

1.. X. Cheng and Z. Shen, Randers metrics of scalar flag curvature, submitted to Journal of the Australian Mathematical Society , March 14, 2007.  

 

d.     Articles in Preprint or Preparation

 

1.      Z. Shen and G. C. Yildirim, A characterization of Randers metrics of scalar flag curvature, preprint.

2.      B. Li and Z. Shen, On projectively flat fourth root metrics, preprint.

 

e.    Survey Articles

     

1.   Z. Shen, Landsberg curvature, S-curvature and Riemann curvature, In “A Sampler  of Finsler Geometry”,  ed. Bao-Bryant-Chern-Shen,  MSRI Publication Series 50, Cambridge University Press, 2004 (303-355).  MR2132662(2005k:53132).

2.   S. Bacso, X. Cheng and Z. Shen, Curvature properties of (α,β)-metrics, In “Finsler Geometry, Sapporo 2005-In Memory of Makoto Matsumoto, ed. S. Sabau and H. Shimada, Advanced Studies in Pure Mathematics 48,  Mathematical Society of Japan, (2007), 73-110.

3.   Z. Shen and C. Sormani, The topology of open manifolds with nonnegative Ricci curvature, the Proceedings of 2006 Midwest Geometry Conference, International Journal of Geometry and Topology.

 

f.   Other Interests

 

1.   J. Chen, G. Bai, Z. Shen, X. Li, D. Fulton and A. Hsu, Prediction of Failure Rate of Rotary Machine Using Monte Carlo Simulations, 2003.

2.    Z. Shen, Elementary Mathematics for Junior High School Students, 268 pages, preprint.

3.   Z. Shen, Problems with solutions for math competitions, 210 pages, preprint.

 

g.   Books and Monographs

 

1. D. Bao, S. S. Chern and Z. Shen, An introduction to Finsler geometry, Graduate Texts in Mathematics 200, Springer-Verlag, New York, 2000, xx+431 pp. $49.95. ISBN 0-387-98948-X. Math Review 2001g:53130

2. Z. Shen, Differential Geometry of Spray and Finsler Spaces. Kluwer Academic Publishers, (2001), 258 pages.

3. Z. Shen, Lectures on Finsler Geometry, World Scientific Publishing Co.,  Singapore, 2001. xiv+ 307 pp. $64.00. ISBN 981-02-4531-9. Math. Review 2002f:53032

4. S.S. Chern and Z. Shen, Riemann-Finsler Geometry, World Scientific Publishers, 2005. MR2169595 (2006d:53094).

    

 

h.   Books Edited

 

1.  D. Bao, S.S. Chern and Z. Shen, Finsler geometry, Contemporary Mathematics, 196, American Mathematical Society, Providence, RI, 1996, xxiv+310 pp. $61. ISBN 0-8218-0507-X. Math. Review 97b:53001

2.  D. Bao, R. Bryant, S.S. Chern and Z. Shen, A Sampler of Finsler Geometry, MSRI Publication Series 50, Cambridge University Press, 2004.  ISBN: 0521831814 (hardcover). MR2132655 (2005j:53003).