共查询到20条相似文献,搜索用时 795 毫秒
1.
Jishan Fan Hongjun Gao Takayoshi Ogawa Futoshi Takahashi 《Mathematische Nachrichten》2012,285(16):1963-1968
We consider the regularity problem under the critical condition to the biharmonic map heat flow from ?4 to a smooth compact Riemannian manifold without boundary. Using Gagliardo‐Nirenberg inequalities and delicate estimates, the Serrin type regularity criterion for the smooth solutions of biharmonic map heat flow is obtained without assuming a smallness condition on the initial energy. Our result improved the results of Lamm in 5 and 6 and generalized the results of Chang, Wang, Yang 1 , Strzelecki 11 and Wang 13 , 14 to non‐stationary case. 相似文献
2.
Jürgen Jost Xiaowei Peng Guofang Wang 《Calculus of Variations and Partial Differential Equations》1996,4(3):205-218
The Seiberg-Witten equations that have recently found important applications for four-dimensional geometry are the Euler-Lagrange equations for a functional involving a connection A on a line bundleL and a section of another bundleW
+ constructed fromL and a spinor bundle on a given four-dimensional Riemannian manifold. We show the regularity of weak solutions and the Palais-Smale condition for this functional. 相似文献
3.
Qun Chen 《Calculus of Variations and Partial Differential Equations》1999,8(2):91-107
In this paper, we consider the harmonic maps with potential from compact Riemannian manifold with boundary into a convex
ball in any Riemannian manifold. We will establish some general properties such as the maximum principles, uniqueness and
existence for these maps, and as an application of them, we derive existence and uniqueness result for the Dirichlet problem
of the Landau-Lifshitz equations.
Received: December 10, 1997 / Accepted: June 29, 1998 相似文献
4.
A variational approach to the regularity of minimal surfaces of annulus type in Riemannian manifolds
Hwajeong Kim 《Differential Geometry and its Applications》2007,25(5):466-484
Given two Jordan curves in a Riemannian manifold, a minimal surface of annulus type bounded by these curves is described as the harmonic extension of a critical point of some functional (the Dirichlet integral) in a certain space of boundary parametrizations. The H2,2-regularity of the minimal surface of annulus type will be proved by applying the critical points theory and Morrey's growth condition. 相似文献
5.
We give a necessary and sufficient condition for a set of left invariant metrics on a compact Heisenberg manifold to be relatively compact in the corresponding moduli space. 相似文献
6.
Takeshi Isobe 《Journal of Geometric Analysis》1998,8(3):447-463
We study the regularity of harmonic maps from Riemannian manifold into a static Lorentzian manifold. We show that when the
domain manifold is two-dimensional, any weakly harmonic map is smooth. We also show that when dimension n of the domain manifold
is greater than two, there exists a weakly harmonic map for the Dirichlet problem which is smooth except for a closed set
whose (n − 2)-dimensional Hausdorff measure is zero. 相似文献
7.
Following Bernicot (2012) [7], we introduce a notion of paraproducts associated to a semigroup. We do not use Fourier transform arguments and the background manifold is doubling, endowed with a sub-Laplacian structure. Our main result is a paralinearization theorem in a non-Euclidean framework, with an application to the propagation of regularity for some nonlinear PDEs. 相似文献
8.
We present a result on trajectories of a Lagrangian system joining two given submanifolds of a Riemannian manifold, under the action of an unbounded potential. As an application, we consider geodesics in a class of semi-Riemannian manifolds, the Plane Wave type spacetimes. 相似文献
9.
In order to apply variational methods to the action functional for geodesics of a stationary spacetime, some hypotheses, useful to obtain classical Palais-Smale condition, are commonly used: pseudo-coercivity, bounds on certain coefficients of the metric, etc. We prove that these technical assumptions admit a natural interpretation for the conformal structure (causality) of the manifold. As a consequence, any stationary spacetime with a complete timelike Killing vector field and a complete Cauchy hypersurface (thus, globally hyperbolic), is proved to be geodesically connected. 相似文献
10.
We prove a general form of a fixed point theorem for mappings from a Riemannian manifold into itself which are obtained as perturbations of a given mapping by means of general operations which in particular include the cases of sum (when a Lie group structure is given on the manifold) and composition. In order to prove our main result we develop a theory of proximal calculus in the setting of Riemannian manifolds. 相似文献
11.
Combining elements of the b-calculus and the theory of elliptic boundary value problems, we solve the gluing problem for b-determinants
of Dirac type operators on manifolds with cylindrical ends. As a corollary of our proof, we derive a gluing formula for the
b-eta invariant and also a relative invariant formula relating the b-spectral invariants on a manifold with cylindrical end
to the spectral invariants with the augmented APS boundary condition on the corresponding compact manifold with boundary. 相似文献
12.
We prove that the constant maps are the onlyp-harmonic maps for anyp 2 from an arbitrary compact Riemannian manifold into a complete Riemannian manifold which admits a strictly convex function. 相似文献
13.
Xianzhe Dai 《Transactions of the American Mathematical Society》2002,354(1):107-122
We prove an adiabatic limit formula for the eta invariant of a manifold with boundary. The eta invariant is defined using the Atiyah-Patodi-Singer boundary condition and the underlying manifold is fibered over a manifold with boundary. Our result extends the work of Bismut-Cheeger to manifolds with boundary.
14.
Roger Moser 《manuscripta mathematica》2001,105(3):379-399
We prove existence and uniqueness of weakly harmonic maps from the unit ball in ℝ
n
(with n≥ 3) to a smooth compact target manifold within the class of maps with small scaled energy for suitable boundary data.
Received: 9 June 2000 / Revised version: 17 April 2001 相似文献
15.
Bifurcation of fixed points from a manifold of trivial fixed points in the infinite-dimensional case
Massimo Furi Mario Martelli Maria Patrizia Pera 《Journal of Fixed Point Theory and Applications》2007,2(2):293-312
We obtain a necessary as well as a sufficient condition for the existence of bifurcation points of a coincidence equation,
and, in particular, of a parametrized fixed point problem. In both cases the trivial solutions are assumed to form a finite-dimensional
submanifold of a Banach manifold. An application is given to a delay differential equation on a manifold: we detect periodic
solutions that rotate close to an equilibrium point.
To Albrecht Dold and Edward Fadell, superb mathematicians and first rate friends 相似文献
16.
Michael Struwe 《manuscripta mathematica》1998,96(4):463-486
Harmonic maps from B
1 (0, ℝ3) to a smooth compact target manifold N with uniformly small scaled energy (see assumption (2) below) are shown to be unique for their boundary values.
Received: 12 May 1997 相似文献
17.
Ana Hurtado 《Differential Geometry and its Applications》2008,26(3):227-243
The aim of this paper is to study the stability of the characteristic vector field of a compact K-contact manifold with respect to the energy and volume functionals when we consider on the manifold a two-parameter variation of the metric. First of all, we multiply the metric in the direction of the characteristic vector field by a constant and then we change the metric by homotheties. We will study to what extent the results obtained in [V. Borrelli, Stability of the characteristic vector field of a Sasakian manifold, Soochow J. Math. 30 (2004) 283-292. Erratum on the article: Stability of the characteristic vector field of a Sasakian manifold, Soochow J. Math. 32 (2006) 179-180] for Sasakian manifolds are valid for a general K-contact manifold. Finally, as an example, we will study the stability of Hopf vector fields on Berger spheres when we consider homotheties of Berger metrics. 相似文献
18.
Roger Moser 《Mathematische Zeitschrift》2003,243(2):263-289
Let be open and a smooth, compact Riemannian manifold without boundary. We consider the approximated harmonic map equation for maps , where . For , we prove H?lder continuity for weak solution s which satisfy a certain smallness condition. For , we derive an energy estimate which allows to prove partial regularity for stationary solutions of the heat flow for harmonic
maps in dimension .
Received: 7 May 2001; / in final form: 22 February 2002 Published online: 2 December 2002 相似文献
19.
Yoonweon Lee 《Journal of Geometric Analysis》2006,16(4):633-660
In this article we discuss the asymptotic expansions of the zeta-determinants of Dirac Laplacians on a compact manifold with
boundary when the boundary part is stretched. In [12] the author studied the same question under the assumption of no existence
of L2 - and extended L2 -solutions of Dirac operators when the boundary part is stretched to infinite length. Therefore, the results in this article
generalize those in [12]. Using the main results we obtain the formula describing the ratio of two zeta-determinants of Dirac
Laplacians with the APS boundary conditions associated with two unitary involutions σ1 and σ2 on ker B satisfying Gσi = -σi G. We also prove the adiabatic decomposition formulas for the zeta-determinants of Dirac Laplacians on a closed manifold
when the Dirichlet or the APS boundary condition is imposed on partitioned manifolds, which generalize the results in [10]
and [11]. 相似文献
20.
Xiaohuan Mo 《Differential Geometry and its Applications》2009,27(1):7-14
One of fundamental problems in Finsler geometry is to establish some delicate equations between Riemannian invariants and non-Riemannian invariants. Inspired by results due to Akbar-Zadeh etc., this note establishes a new fundamental equation between non-Riemannian quantity H and Riemannian quantities on a Finsler manifold. As its application, we show that all R-quadratic Finsler metrics have vanishing non-Riemannian invariant H generalizing result previously only known in the case of Randers metric. 相似文献