共查询到20条相似文献,搜索用时 31 毫秒
1.
Derchyi Wu 《Annals of Global Analysis and Geometry》1997,15(2):133-139
We prove an existing theorem of homotopic harmonic diffeomorphisms between complete surfaces of finite total curvature and nontrivial genus. This is a generalization of a theorem of Jost and Schoen [4]. 相似文献
2.
We study partially hyperbolic attractors ofC 2 diffeomorphisms on a compact manifold. For a robust (non-empty interior) class of such diffeomorphisms, we construct Sinai-Ruelle-Bowen measures, for which we prove exponential decay of correlations and the central limit theorem, in the space of Hölder continuous functions. The techniques we develop (backward inducing, redundancy elimination algorithm) should be useful in the study of the stochastic properties of much more general non-uniformly hyperbolic systems. 相似文献
3.
We establish existence and uniqueness theorems for V-harmonic maps from complete noncompact manifolds. This class of maps includes Hermitian harmonic maps, Weyl harmonic maps, affine harmonic maps, and Finsler harmonic maps from a Finsler manifold into a Riemannian manifold. We also obtain a Liouville type theorem for V-harmonic maps. In addition, we prove a V-Laplacian comparison theorem under the Bakry-Emery Ricci condition. 相似文献
4.
HONGXIA LI 《Proceedings Mathematical Sciences》2014,124(3):437-445
In this paper, we study the periodic diffeomorphisms on homotopy E(4) surfaces. Under some conditions, we prove the non-existence of periodic diffeomorphisms of odd prime order that act trivially on the cohomology of elliptic surfaces E(4). Besides, we give an application of our main theorem. 相似文献
5.
We obtain Becker type univalence conditions for locally univalent harmonic mappings defined in one of the following domains: the unit disc, a halfplane, the exterior of the unit disc and prove a generalization of John’s univalence condition. 相似文献
6.
7.
Clark Robinson 《Journal of Differential Equations》1976,22(1):28-73
In this paper we prove that if f is a C1 diffeomorphism that satisfies Axiom A and the strong transversality condition then it is structurally stable. J. Robbin proved this theorem for C2 diffeomorphisms. In addition to reducing the amount of differentiability necessary to prove the theorem, we also give a new proof combining the df metric of Robbin with the stable and unstable manifold proof of D. Anosov. We also prove structural stability in the neighborhood of a single hyperbolic basic set (independent of its being part of a diffeomorphism that satisfies Axiom A and the strong transversality condition). These proofs are adapted to prove the structural stability of C1 flows in another paper. 相似文献
8.
《Mathematische Nachrichten》2017,290(13):2024-2051
We prove a genuine analogue of the Wiener Tauberian theorem for , where G is a real rank one noncompact, connected, semisimple Lie group with finite centre. This generalizes the corresponding result on the automorphism group of the unit disk by Y. Ben Natan, Y. Benyamini, H. Hedenmalm, and Y. Weit. We extend this result for hypergeometric transforms and as an application we prove an analogue of Furstenberg theorem on harmonic functions for hypergeometric transforms. 相似文献
9.
Using probabilistic methods, we prove new rigidity results for groups and pseudo-groups of diffeomorphisms of one dimensional
manifolds with intermediate regularity class (i.e. between C
1 and C
2). In particular, we show some generalizations of Denjoy theorem and the classical Kopell lemma for abelian groups. These
techniques are also applied to the study of codimension-1 foliations. For instance, we obtain several generalized versions
of Sacksteder theorem in class C
1. We conclude with some remarks about the stationary measure. 相似文献
10.
In this paper, we will introduce the notion of harmonic stability for complete minimal hypersurfaces in a complete Riemannian
manifold. The first result we prove, is that a complete harmonic stable minimal surface in a Riemannian manifold with non-negative
Ricci curvature is conformally equivalent to either a plane R
2 or a cylinder R × S
1, which generalizes a theorem due to Fischer-Colbrie and Schoen [12].
The second one is that an n ≥ 2-dimensional, complete harmonic stable minimal, hypersurface M in a complete Riemannian manifold with non-negative sectional curvature has only one end if M is non-parabolic. The third one, which we prove, is that there exist no non-trivial L
2-harmonic one forms on a complete harmonic stable minimal hypersurface in a complete Riemannian manifold with non-negative
sectional curvature. Since the harmonic stability is weaker than stability, we obtain a generalization of a theorem due to
Miyaoka [20] and Palmer [21].
Research partially Supported by a Grant-in-Aid for Scientific Research from the Ministry of Education, Culture, Sports, Science
and Technology, Japan.
The author’s research was supported by grant Proj. No. KRF-2007-313-C00058 from Korea Research Foundation, Korea.
Authors’ addresses: Qing-Ming Cheng, Department of Mathematics, Faculty of Science and Engineering, Saga University, Saga
840-8502, Japan; Young Jin Suh, Department of Mathematics, Kyungpook National University, Taegu 702-701, South Korea 相似文献
11.
In this paper, we mainly study the Rm (m>0) Riemann boundary value problems for functions with values in a Clifford algebra C?(V3, 3). We prove a generalized Liouville‐type theorem for harmonic functions and biharmonic functions by combining the growth behaviour estimates with the series expansions for k‐monogenic functions. We obtain the result under only one growth condition at infinity by using the integral representation formulas for harmonic functions and biharmonic functions. By using the Plemelj formula and the integral representation formulas, a more generalized Liouville theorem for harmonic functions and biharmonic functions are presented. Combining the Plemelj formula and the integral representation formulas with the above generalized Liouville theorem, we prove that the Rm (m>0) Riemann boundary value problems for monogenic functions, harmonic functions and biharmonic functions are solvable. Explicit representation formulas of the solutions are given. Copyright © 2009 John Wiley & Sons, Ltd. 相似文献
12.
We study Morse--Smale diffeomorphisms of n-manifolds with four periodic points which are the only periodic points. We prove that for n= 3 these diffeomorphisms are gradient-like and define a class of diffeomorphisms inevitably possessing a nonclosed heteroclinic curve. For n 4, we construct a complete conjugacy invariant in the class of diffeomorphisms with a single saddle of codimension one. 相似文献
13.
We consider a kind of generalized harmonic maps, namely, the VT-harmonic maps. We prove an existence theorem for the Dirichlet problem of VT-harmonic maps from compact manifolds with boundary.
相似文献14.
T. Hilberdink 《Archiv der Mathematik》2001,77(4):354-359
In this paper we prove a complex Tauberian theorem for functions analytic in the open unit disc.The method used is based on Cauchy's integral formula for the Taylor coefficients. We show how a Blackwell type renewal theorem is an easy consequence of our main result. 相似文献
15.
We prove two Dyakonov type theorems which relate the modulus of continuity of a function on the unit disc with the modulus of continuity of its absolute value. The methods we use are quite elementary, they cover the case of functions which are quasiregular and harmonic, briefly hqr, in the unit disc. 相似文献
16.
Manuel D. Contreras Santiago Díaz-Madrigal 《Journal of Mathematical Analysis and Applications》2021,493(1):124525
We prove that topological evolution families on a Riemann surface S are rather trivial unless S is conformally equivalent to the unit disc or the punctuated unit disc. We also prove that, except for the torus where there is no non-trivial continuous Loewner chain, there is a topological evolution family associated to any topological Loewner chain and, conversely, any topological evolution family comes from a topological Loewner chain on the same Riemann surface. 相似文献
17.
Peter Haı̈ssinsky 《Comptes Rendus Mathematique》2002,334(8):635-638
We prove that the Calabi invariant for the symplectic diffeomorphisms of the unit disk with compact support is well defined for quasiconformal maps and depends continuously with respect to these homeomorphisms in the quasiconformal topology. To cite this article: P. Ha??ssinsky, C. R. Acad. Sci. Paris, Ser. I 334 (2002) 635–638. 相似文献
18.
Armando Castro 《Bulletin of the Brazilian Mathematical Society》2011,42(3):455-483
We prove some criteria for uniform hyperbolicity based on the periodic points of the transformation. More precisely, if a mild hyperbolicity condition holds for the periodic points of any diffeomorphism in a residual subset of a C 1-open set U then there exists an open and dense subset A ? U of Axiom A diffeomorphisms. Moreover, we also prove a noninvertible version of Ergodic Closing Lemma which we use to prove a counterpart of this result for local diffeomorphisms. 相似文献
19.
We prove a C1-connecting lemma for pseudo-orbits of diffeomorphisms on compact manifolds. We explore some consequences for C1-generic diffeomorphisms. For instance, C1-generic conservative diffeomorphisms are transitive. To cite this article: C. Bonatti, S. Crovisier, C. R. Acad. Sci. Paris, Ser. I 336 (2003). 相似文献
20.
Heiko von der Mosel Sven Winklmann 《Annales de l'Institut Henri Poincaré (C) Analyse Non Linéaire》2009
We prove global C0,α-estimates for harmonic maps from Finsler manifolds into regular balls of Riemannian target manifolds generalizing results of Giaquinta, Hildebrandt, and Hildebrandt, Jost and Widman from Riemannian to Finsler domains. As consequences we obtain a Liouville theorem for entire harmonic maps on simple Finsler manifolds, and an existence theorem for harmonic maps from Finsler manifolds into regular balls of a Riemannian target. 相似文献