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81.
Songting YIN 《Frontiers of Mathematics in China》2018,13(2):435-448
We obtain the Laplacian comparison theorem and the Bishop-Gromov comparison theorem on a Finsler manifold with the weighted Ricci curvature Ric∞ bounded below. As applications, we prove that if the weighted Ricci curvature Ric∞ is bounded below by a positive number, then the manifold must have finite fundamental group, and must be compact if the distortion is also bounded. Moreover, we give the Calabi-Yau linear volume growth theorem on a Finsler manifold with nonnegative weighted Ricci curvature. 相似文献
82.
Let be a complete Riemannian manifold with , and let be two complete totally geodesic submanifolds in M. We prove that if n1 + n2 = n − 2 and if the distance , then Mi is isometric to , or with the canonical metric when ni>0, and thus, M is isometric to , or except possibly when n = 3 and M1 (or M2) with or n = 4 and M1 (or M2) . 相似文献
83.
Romain Lagrange 《力学快报》2013,3(6):061001
We study the buckling of a one fiber composite whose matrix stiffness is slightly dependent on the compressive force. We show that the equilibrium curves of the system exhibit a limit load when the induced stiffness parameter gets bigger than a threshold. This limit load increases when the stiffness parameter is increasing and it is related to a possible localized path in the post-buckling domain. Such a change in the maximum load may be very desirable from a structural stand point. 相似文献
84.
We study the injectivity radius bound for 3-d Ricci flow with bounded curvature. As applications, we show the long time existence of the Ricci flow with positive Ricci curvature and with curvature decay condition at infinity. We partially settle a question of Chow-Lu-Ni [Hamilton’s Ricci Flow, p. 302]. 相似文献
85.
86.
87.
Yawei CHU 《Frontiers of Mathematics in China》2012,7(1):19-27
Let (M
n
, g) be an n-dimensional complete noncompact Riemannian manifold with harmonic curvature and positive Sobolev constant. In this paper,
by employing an elliptic estimation method, we show that (M
n
, g) is a space form if it has sufficiently small L
n/2-norms of trace-free curvature tensor and nonnegative scalar curvature. Moreover, we get a gap theorem for (M
n
, g) with positive scalar curvature. 相似文献
88.
LIU Shi-Da SHI Shao-Ying LIU Shi-Kuo FU Zun-Tao LIANG Fu-Ming XIN Guo-Jun 《理论物理通讯》2005,43(4):604-606
The vortex is a common phenomenon in
fluid field. In this paper, vortex can be represented by curvature
c, which varies with arc length s. The variance of point
(x,y) with arc length in stream line satisfies a 2-order
variable-coefficient linear ordinary differential equation. The
type vortex can be analyzed qualitatively by this ordinary
differential equation. 相似文献
89.
We use a new method to construct a class of asymptotically locally flat, scalar flat metrics. These metrics were constructed via algebraic geometry method by LeBrun before and provide counterexamples to the generalized positive action conjecture of Hawking and Pope. 相似文献
90.
The solitary wave and wave front are two
important behaviors of nonlinear evolution equations.
Geometrically, solitary wave and wave front are all plane curve.
In this paper, they can be represented in terms of curvature
c(s), which varies with arc length s. For solitary wave when
s → ±∞, then its curvature c(s) approaches
zero, and when s=0, the curvature c(s) reaches its maximum.
For wave front, when s → ±∞, then its
curvature c(s) approaches zero, and when s=0, the curvature
c(s) is still zero, but c'(s) ≠ 0. That is, s=0 is a
turning point. When c(s) is given, the variance at some point
(x,y) in stream line with arc length s satisfies a 2-order
linear variable-coefficient ordinary differential equation. From
this equation, it can be determined qualitatively whether the
given curvature is a solitary wave or wave front. 相似文献