共查询到20条相似文献,搜索用时 11 毫秒
1.
T. Rapcsák 《Journal of Optimization Theory and Applications》2005,127(1):165-176
Some properties of the spaces of paths are studied in order to define and characterize the local convexity of sets belonging
to smooth manifolds and the local convexity of functions defined on local convex sets of smooth manifolds.
This paper is dedicated to the memory of Guido Stampacchia. This research was supported in part by the Hungarian Scientific
Research Fund, Grants OTKA-T043276 and OTKA-T043241, and by CNR, Rome, Italy. 相似文献
2.
Roberto Frigerio 《Geometriae Dedicata》2006,118(1):105-131
Suppose
, let M
1, M
2 be n-dimensional connected complete finite-volume hyperbolic manifolds with nonempty geodesic boundary, and suppose that π1 (M
1) is quasi-isometric to π1 (M
2) (with respect to the word metric). Also suppose that if n=3, then ∂M
1 and ∂M
2 are compact. We show that M
1 is commensurable with M
2. Moreover, we show that there exist homotopically equivalent hyperbolic 3-manifolds with non-compact geodesic boundary which are not commensurable with each other. We also prove that if M is as M
1 above and G is a finitely generated group which is quasi-isometric to π1 (M), then there exists a hyperbolic manifold with geodesic boundary M′ with the following properties: M′ is commensurable with M, and G is a finite extension of a group which contains π1 (M′) as a finite-index subgroupMathematics Subject Classification (2000). Primary: 20F65; secondary: 30C65, 57N16 相似文献
3.
A. V. Bolsinov 《Journal of Mathematical Sciences》2004,123(4):4185-4197
We discuss the notion of geodesics and study the global behavior of geodesics on closed Riemannian manifolds. In particular, we emphasize the case of so-called integrable geodesic flows. 相似文献
4.
Rossella Bartolo Anna Germinario Miguel Sánchez 《Annals of Global Analysis and Geometry》2002,21(1):63-84
In this paper the problem of the geodesic connectedness and convexity ofincomplete Riemannian manifolds is analyzed. To this aim, a detailedstudy of the notion of convexity for the associated Cauchy boundary iscarried out. In particular, under widely discussed hypotheses,we prove the convexity of open domains (whose boundaries may benondifferentiable) of a complete Riemannian manifold. Variationalmethods are mainly used. Examples and applications are provided,including a result for dynamical systems on the existence oftrajectories with fixed energy. 相似文献
5.
In this paper we describe a function F n : R + → R + such that for any hyperbolic n-manifold M with totally geodesic boundary ${\partial M \neq \emptyset}In this paper we describe a function F
n
: R
+ → R
+ such that for any hyperbolic n-manifold M with totally geodesic boundary ?M 1 ?{\partial M \neq \emptyset} , the volume of M is equal to the sum of the values of F
n
on the orthospectrum of M. We derive an integral formula for F
n
in terms of elementary functions. We use this to give a lower bound for the volume of a hyperbolic n-manifold with totally
geodesic boundary in terms of the area of the boundary. 相似文献
6.
In this paper, we generalize geodesic $E$-convex function and define geodesic $\gamma$-pre-$E$-convex and geodesic $\gamma$-$E$-convex functions on Riemannian manifolds. The sufficient condition of equivalence class of geodesic $\gamma$-pre-$E$-convexity and geodesic $\gamma$-$E$-convexity for differentiable function on Riemannian manifolds is studied. We discuss the sufficient condition for $E$-epigraph to be geodesic $E$-convex set. At the end, we establish some optimality results with the aid of geodesic $\gamma$-pre-$E$-convex and geodesic $\gamma$-$E$-convex functions and discuss the mean value inequality for geodesic $\gamma$-pre-$E$-convex function. 相似文献
7.
In a Hadamard manifold with sectional curvaturebounded from below by –k
2
2, we give sharp upper estimates for the difference circumradius minus inradiusof a compact k
2-convex domain, and we getalso estimates for the quotient (Total d-mean curvature)/Area of a convex domain. 相似文献
8.
In this paper, a relationship between a vector variational inequality and a vector optimization problem is given on a Hadamard manifold. An existence of a weak minimum for a constrained vector optimization problem is established by an analogous to KKM lemma on a Hadamard manifold. 相似文献
9.
D'Atri and Nickerson [6], [7] have given necessary conditions for the geodesic symmetries of a Riemannian manifold to preserve the volume element. We use their results to show that ifG is a compact simple Lie group,T is a maximal torus ofG, andG/T is not symmetric, then anyG-invariant Kähler metric onG/T does not have volume-preserving geodesic symmetries. From the Kähler/de Rham decomposition of a compact homogeneous Kähler manifold [8], our result extends to the invariant Kähler metrics on a quotient of a compact connected Lie group by a maximal torus. In proving these results we compute directly the Ricci tensor of anyG-invariant Kähler metric onG/T forG compact connected andT a maximal torus ofG. The result is an explicit formula giving the value of the Ricci tensor elements in terms of the root structure of the Lie algebra ofG. 相似文献
10.
本文用Hadamard方法为一类带有非线性项R:D(A)→H的无限维耗散动力系统建立惯性流形.在建立惯性流形的过程中,系统的一种“不变锥性质”被充分利用着.这里,对惯性流形存在性至关紧要的谱间隙条件是. 相似文献
11.
Liu Qingmin 《东北数学》1995,(1)
ConstructionofInertialManifoldsbytheHadamardMethodLiuQingmin(刘青民)(DepartmentofMathematics,LanzhouUniversity,Lanzhou,730000)Ab... 相似文献
12.
利用 Finsler流形中的切曲率和旗曲率 ,研究了距离函数与测地球的凸性 ;指出了在单连通完备 Minkowski空间中测地球正好是平面的一部分 相似文献
13.
Feng-Yu Wang 《Potential Analysis》2014,41(3):699-714
To study the reflecting diffusion processes on manifolds with boundary, some new curvature operators are introduced by using the Bakry-Emery curvature and the second fundamental form. As applications, the gradient estimates, log-Harnack inequality and Poincaré/log-Sobolev inequalities are investigated for the Neumann semigroup on manifolds with boundary. 相似文献
14.
15.
Chong Li Genaro López Victoria Martín-Márquez Jin-Hua Wang 《Set-Valued and Variational Analysis》2011,19(3):361-383
Firmly nonexpansive mappings are introduced in Hadamard manifolds, a particular class of Riemannian manifolds with nonpositive
sectional curvature. The resolvent of a set-valued vector field is defined in this setting and by means of this concept, a
strong relationship between monotone vector fields and firmly nonexpansive mappings is established. This fact is then used
to prove that the resolvent of a maximal monotone vector field has full domain. The Yosida approximation of a set-valued vector
field is also introduced, analyzing its properties from which the asymptotic behavior of the resolvent is studied. Regarding
the singularities of a set-valued monotone vector field, existence results are proved under certain boundary condition. As
a consequence, the existence of fixed points for continuous pseudo-contractive mappings is obtained. 相似文献
16.
We study the filling invariants at infinity div
k
for Hadamard manifolds defined by Brady and Farb [ Trans. Am. Math. Soc. 350(8) (1998), 3393–3405]. Among other results, we give a positive answer to the question they posed: whether these invariants
can be used to detect the rank of a symmetric space of noncompact type. 相似文献
17.
A. Zeghib 《Geometric And Functional Analysis》1999,9(4):823-854
This is part II of a series on noncompact isometry groups of Lorentz manifolds. We have introduced in part I, a compactification
of these isometry groups, and called "bipolarized" those Lorentz manifolds having a "trivial" compactification. Here we show
a geometric rigidity of non-bipolarized Lorentz manifolds; that is, they are (at least locally) warped products of constant
curvature Lorentz manifolds by Riemannian manifolds.
Submitted: April 1998, final version: November 1998. 相似文献
18.
19.
In this paper, we develop a projection-type algorithm for set-valued variational inequalities on Hadamard manifolds. The proposed method is well defined whether the solution set of the problem is non-empty or not. Under pseudomonotonicity assumptions on the underlying vector field, our method is convergent to a solution of the given set-valued variational inequality. The results presented in this paper generalize and improve some known results introduced by Tang et al. (Optimization 64(5):1081–1096, 2015). 相似文献
20.
《数学研究通讯:英文版》2016,(2):97-104
In this note, we prove a concentration theorem of (R, p)-anders. As a simple corollary, one can prove that (X, p)-anders do not admit coarse embeddings into Hadamard manifolds with bounded sectional curvatures. 相似文献