共查询到20条相似文献,搜索用时 31 毫秒
1.
Here we consider initial boundary value problem for the time–fractional diffusion equation by using the single layer potential
representation for the solution. We derive the equivalent boundary integral equation. We will show that the single layer potential
admits the usual jump relations and discuss the mapping properties of the single layer operator in the anisotropic Sobolev
spaces. Our main theorem is that the single layer operator is coercive in an anisotropic Sobolev space. Based on the coercivity
and continuity of the single layer operator we finally show the bijectivity of the operator in a certain range of anisotropic
Sobolev spaces.
相似文献
2.
Jiezhu Lin 《Mathematische Zeitschrift》2011,267(1-2):81-108
The article gives a necessary and sufficient condition for a Frobenius manifold to be a CDV-structure. We show that there exists a positive definite CDV-structure on any semi-simple Frobenius manifold. We also compare three natural connections on a CDV-structure and conclude that the underlying Hermitian manifold of a non-trivial CDV-structure is not a K?hler manifold. Finally, we compute the harmonic potential of a harmonic Frobenius manifold. 相似文献
3.
Mark McLean 《Geometric And Functional Analysis》2012,22(2):369-442
We will show that the cotangent bundle of a manifold whose free loopspace homology grows exponentially is not symplectomorphic to any smooth affine variety. We will also show that the unit cotangent bundle of such a manifold is not Stein fillable by a Stein domain whose completion is symplectomorphic to a smooth affine variety. For instance, these results hold for end connect sums of simply connected manifolds whose cohomology with coefficients in some field has at least two generators. We use an invariant called the growth rate of symplectic homology to prove this result. 相似文献
4.
In this paper, we study the existence of a complete holomorphic vector field on a strongly pseudoconvex complex manifold admitting a negatively curved complete Kähler–Einstein metric and a discrete sequence of automorphisms. Using the method of potential scaling, we will show that there is a potential function of the Kähler–Einstein metric whose differential has a constant length. Then, we will construct a complete holomorphic vector field from the gradient vector field of the potential function.
相似文献5.
6.
《Optimization》2012,61(2):257-270
Abstract In this paper we consider the minimization problem with constraints. We will show that if the set of constraints is a Riemannian manifold of nonpositive sectional curvature, and the objective function is convex in this manifold, then the proximal point method in Euclidean space is naturally extended to solve that class of problems. We will prove that the sequence generated by our method is well defined and converge to a minimizer point. In particular we show how tools of Riemannian geometry, more specifically the convex analysis in Riemannian manifolds, can be used to solve nonconvex constrained problem in Euclidean, space. 相似文献
7.
Ya. M. Dymarskii 《Ukrainian Mathematical Journal》1996,48(6):866-879
We consider a family of boundary-value problems with some potential as a parameter. We study the manifold of normalized eigenfunctions with even number of zeros in a period, and the manifold of potentials associated with double eigenvalues. In particular, we prove that the manifold of normalized eigenfunctions is a trivial fiber space over a unit circle and that the manifold of potentials with double eigenvalues is a homotopically trivial manifold trivially imbedded into the space of potentials. 相似文献
8.
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
9.
Mixed elliptic boundary value problems are characterised by conditions which have a jump along an interface of codimension 1 on the boundary. We study such problems in weighted edge spaces and show the Fredholm property and the existence of parametrices under additional conditions of trace and potential type on the interface. We develop a new method for computing the interface conditions in terms of the index of boundary value problems in weighted spaces on infinite cones, combined with structures from the calculus of boundary value problems on a manifold with edges. This will be illustrated by the Zaremba problem and other mixed problems for the Laplace operator. The approach itself is completely general. 相似文献
10.
A locally conformally Kähler (LCK) manifold M is one which is covered by a Kähler manifold ${\widetilde M}A locally conformally K?hler (LCK) manifold M is one which is covered by a K?hler manifold [(M)\tilde]{\widetilde M} with the deck transformation group acting conformally on [(M)\tilde]{\widetilde M}. If M admits a holomorphic flow, acting on [(M)\tilde]{\widetilde M} conformally, it is called a Vaisman manifold. Neither the class of LCK manifolds nor that of Vaisman manifolds is stable
under small deformations. We define a new class of LCK-manifolds, called LCK manifolds with potential, which is closed under
small deformations. All Vaisman manifolds are LCK with potential. We show that an LCK-manifold with potential admits a covering
which can be compactified to a Stein variety by adding one point. This is used to show that any LCK manifold M with potential, dim M ≥ 3, can be embedded into a Hopf manifold, thus improving similar results for Vaisman manifolds Ornea and Verbitsky (Math
Ann 332:121–143, 2005). 相似文献
11.
《Applied Mathematics Letters》2003,16(5):715-721
In this note, we study Hele-Shaw flows in the presence of anisotropic surface tension when the fluid domain is bounded. The flows are driven by a sink, by a multipole, or solely by anisotropic surface tension. For a sink flow, we show that if the center of mass of the initial domain is not located at a certain point which is determined by the anisotropic surface tension and intensity of the sink, then either the solution will break down before all the fluid is sucked out or the fluid domain will eventually become unbounded in diameter. For a multipole driven flow, we prove that if the anisotropic surface tension, the order, and intensity of the multipole do not satisfy a certain equality, either the flow will develop finite-time singularities or the fluid domain will become unbounded in diameter as time goes to infinity. For a flow driven purely by anisotropic surface tension, we show that the center of mass of the fluid domain moves in a constant velocity, which is determined explicitly. 相似文献
12.
Christopher Lin 《偏微分方程通讯》2013,38(10):1529-1546
The spectrum (of the Dirichlet Laplacian) of non-compact, non-complete Riemannian manifolds is much less understood than their compact counterparts. In particular it is often not even known whether such a manifold has any discrete spectra. In this article, we will prove that a certain type of non-compact, non-complete manifold called the quantum tube has non-empty discrete spectrum. The quantum tube is a tubular neighborhood built about an immersed complete manifold in Euclidean space. The terminology of “quantum” implies that the geometry of the underlying complete manifold can induce discrete spectra – hence quantization. We will show how the Weyl tube invariants appear in determining the existence of discrete spectra. This is an extension and generalization, on the geometric side, of the previous work of the author on the “quantum layer.” 相似文献
13.
Farid Madani Andrei Moroianu Mihaela Pilca 《Annals of Global Analysis and Geometry》2017,51(4):401-417
We study compact toric strict locally conformally Kähler manifolds. We show that the Kodaira dimension of the underlying complex manifold is \(-\infty \), and that the only compact complex surfaces admitting toric strict locally conformally Kähler metrics are the diagonal Hopf surfaces. We also show that every toric Vaisman manifold has lcK rank 1 and is isomorphic to the mapping torus of an automorphism of a toric compact Sasakian manifold. 相似文献
14.
Hirokazu Shimobe 《Geometriae Dedicata》2018,197(1):49-60
We study compact complex manifolds bimeromorphic to locally conformally Kähler (LCK) manifolds. This is an analogy of studying a compact complex manifold bimeromorphic to a Kähler manifold. We give a negative answer for a question of Ornea, Verbitsky, Vuletescu by showing that there exists no LCK current on blow ups along a submanifold (dim \(\ge 1\)) of Vaisman manifolds. We show that a compact complex manifold with LCK currents satisfying a certain condition can be modified to an LCK manifold. Based on this fact, we define a compact complex manifold with a modification from an LCK manifold as a locally conformally class C (LC class C) manifold. We give examples of LC class C manifolds that are not LCK manifolds. Finally, we show that all LC class C manifolds are locally conformally balanced manifolds. 相似文献
15.
Vivina Barutello Susanna Terracini Gianmaria Verzini 《Calculus of Variations and Partial Differential Equations》2014,49(1-2):391-429
For the class of anisotropic Kepler problems in $\mathbb{R }^d\setminus \{0\}$ with homogeneous potentials, we seek parabolic trajectories having prescribed asymptotic directions at infinity and which, in addition, are Morse minimizing geodesics for the Jacobi metric. Such trajectories correspond to saddle heteroclinics on the collision manifold, are structurally unstable and appear only for a codimension-one submanifold of such potentials. We give them a variational characterization in terms of the behavior of the parameter-free minimizers of an associated obstacle problem. We then give a full characterization of such a codimension-one manifold of potentials and we show how to parameterize it with respect to the degree of homogeneity. 相似文献
16.
In this article, we study closed Riemannian manifolds with small excess. We show that a closed connected Riemannian manifold
with Ricci curvature and injectivity radius bounded from below is homeomorphic to a sphere if it has sufficiently small excess.
We also show that a closed connected Riemannian manifold with weakly bounded geometry is a homotopy sphere if its excess is
small enough. 相似文献
17.
Christine Laurent-Thiébaut 《Mathematische Zeitschrift》2010,265(4):761-775
We prove sharp anisotropic Hölder estimates for the local solutions of the tangenital Cauchy-Riemann equation in q-concave CR manifolds and we derive the same kind of estimates for global solutions when the manifold is compact. 相似文献
18.
Liana David 《Differential Geometry and its Applications》2006,24(5):542-553
We introduce and study the notion of Sasaki-Weyl manifold, which is a natural generalization of the notion of Sasaki manifold. We construct a reduction of Sasaki-Weyl manifolds and we show that it commutes with several reductions already existing in the literature. 相似文献
19.
We use a slightly modified version of McGehee's transformation to study the triple collisions of the isosceles three body problem in a way that allows us to let the mass ratio go to zero. We study the limiting case and show that the collision manifold changes topologically, which affects the behaviour of near collision orbits. We also obtain new information about the flow on the collision manifold when the mass ratio is small. 相似文献
20.
We consider an open manifold which is the interior of a compact manifold with boundary. Assuming gauge invariance, we classify
magnetic fields with compact support into being trapping or non-trapping. We study spectral properties of the associated magnetic
Laplacian for a class of Riemannian metrics which includes complete hyperbolic metrics of finite volume. When B is non-trapping, the magnetic Laplacian has nonempty essential spectrum. Using Mourre theory, we show the absence of singular
continuous spectrum and the local finiteness of the point spectrum. When B is trapping, the spectrum is discrete and obeys the Weyl law. The existence of trapping magnetic fields with compact support
depends on cohomological conditions, indicating a new and very strong long-range effect.
In the non-gauge invariant case, we exhibit a strong Aharonov–Bohm effect. On hyperbolic surfaces with at least two cusps,
we show that the magnetic Laplacian associated to every magnetic field with compact support has purely discrete spectrum for
some choices of the vector potential, while other choices lead to a situation of limiting absorption principle.
We also study perturbations of the metric. We show that in the Mourre theory it is not necessary to require a decay of the
derivatives of the perturbation. This very singular perturbation is then brought closer to the perturbation of a potential.
Submitted: February 6, 2007. Accepted: August 20, 2007. 相似文献