Publication List
ZHONGMIN SHEN
January 22, 2012
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.,
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.,
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.,
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.,
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
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, Publicationes Mathematicae,
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
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
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,
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, Publicationes Mathematicae,
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, On a projective
class of Finsler metrics, Publ.
Math. Debrecen, 70(2007), 211-219.
62. 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.
63.
Z. Shen and H. Xing, On Randers metrics of isotropic S-curvature, Acta Mathematica Sinica, English Series, 24(2008), 789-796.
64. Z. Shen and G. C. Yildirim, On a class of
projectively flat metrics with constant flag curvature,
65. X.
Cheng and Z. Shen, A class of Finsler metrics with isotropic
66.
B. Li and Z. Shen,
67. Z.
Shen, On projectively flat (α,β)-metrics, Canadian
Mathematical Bulletin, 52(1)(2009),
132-144
68. Z. Shen, On a class of Landsberg metrics in Finsler Geometry,
69. X. Cheng and Z.
Shen, Randers metrics of scalar flag curvature, Journal of Australian Mathematical Society, 87 (2009), 359-370.
70. B.
Li, Y.B. Shen and Z. Shen, On a class of Douglas metrics in Finsler geometry, Studia Sci. Math. Hungarica, 46(3), (2009), 355-365.
71. X. Cheng, Z. Shen and Y. Zhou, On locally dually
flat Randers metrics, International
Journal of Mathematics, 21 (2010), 1531-1543.
b. Articles
Accepted for Publication
72. B. Li and Z. Shen, On projectively flat fourth root
metrics, Canadian Mathematical Bulletin,
accepted, 2009.
73. Z. Shen,
On some non-Riemannian quantities in Finsler geometry. Canadian Mathematical Bulletin, accepted,
2010.
74. X. Cheng,
Z. Shen and Y. Tian, Einstein (alpha,beta)-metrics, Israel Journal of Mathematics,
accepted, 2011.
75. E. S. Sevim and Z. Shen, Randers metrics of constant scalar curvature,
Canadian Mathematical Bulletin,
accepted, 2011.
76. E. S. Sevim, Z. Shen and L. Zhao, On a class of Ricci-flat Douglas
metrics, International Journal of
Mathematics, accepted, 2011.
c. Articles
Submitted for Publications
1.
Z.Shen and G. C.
Yildirim, A characterization of Randers metrics of scalar flag curvature,
preprint.
2.
E. S. Sevim, Z. Shen and L. Zhao, Some Ricci-flat metrics, preprint,
2011.
3.
B. Chen, Z. Shen and L. Zhao, On a
class of Ricci-flat metrics in Finsler geometry, preprint.
4.
Z. Shen and Q. Xia, Conformal vector fields on Randers manifolds, preprint.
d.
Articles
in Preprint or Preparation
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.,
4. S.S. Chern and Z. Shen, Riemann-Finsler
Geometry, World Scientific Publishers, 2005. MR2169595
(2006d:53094).
5. X. Cheng and
Z. Shen, Finsler Geometry --- An approach via Randers spaces, Springer-Verlag,
to appear.
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. B
3.
Yibing Shen, Zhongmin Shen and S.T. Yau, Differential Gwometry --- under
influence of S.S. Chern,
Springer-Verlag, 2012.