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241.
242.
Baris Coskunuzer 《Mathematische Zeitschrift》2006,252(4):811-824
We show that for any extreme curve in a 3-manifold M, there exist a canonical mean convex hull containing all least area disks spanning the curve. Similar result is true for
asymptotic case in such that for any asymptotic curve , there is a canonical mean convex hull containing all minimal planes spanning Γ. Applying this to quasi-Fuchsian manifolds,
we show that for any quasi-Fuchsian manifold, there exist a canonical mean convex core capturing all essential minimal surfaces.
On the other hand, we also show that for a generic C3-smooth curve in the boundary of C3-smooth mean convex domain in ℝ3, there exist a unique least area disk spanning the curve. 相似文献
243.
Yu. G. Reshetnyak 《Siberian Mathematical Journal》2006,47(1):117-134
We study some classes of functions with values in a complete metric space which can be considered as analogs of the Sobolev spaces W p 1 . Earlier the author considered the case of functions on a domain of ? n . Here we study the general case of mappings on an arbitrary Lipschitz manifold. We give necessary auxiliary facts, consider some examples, and describe some methods of construction of lower semicontinuous functionals on the classes W p 1 (M), where M is a Lipschitz manifold. 相似文献
244.
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
245.
246.
Methods from stochastic analysis are combined with functional analytic methods in order to prove a Feynman–Kac formula för Schrödinger type operators with nonnegative locally square integrable potentials on vector bundles over complete Riemannian manifolds. In particular, we obtain a Feynman–Kac–Itô formula on manifolds for Schrödinger operators with magnetic fields. 相似文献
247.
Daniel Pa?ca 《Physica D: Nonlinear Phenomena》2010,239(16):1516-1766
The present paper studies the escape mechanism in collinear three point mass systems with small-range-repulsive/large-range-attractive pairwise interaction. Specifically, we focus on the asymptotic behaviour for systems with non-negative total energy.On the zero energy level set there are two distinct asymptotic states, called 1+1+1escape configurations, where all the three separations infinitely increase as t→∞. We show that 1+1+1 escapes are improbable by proving that the set of initial conditions leading to such asymptotic configurations has zero Lebesgue measure. When the outer mass points are of the same kind we deduce the existence of a heteroclinic orbit connecting the 1+1+1 escape configurations. We further prove that this orbit is stable under parameter perturbation.In the positive energies’ case, we show that the set of initial conditions leading to 1+1+1 escape configurations has positive Lebesgue measure. 相似文献
248.
Existence of ground state solutions for Kirchhoff‐type problems involving critical Sobolev exponents
《Mathematical Methods in the Applied Sciences》2018,41(1):371-385
In this paper, we study the existence of ground state solutions for a Kirchhoff‐type problem in involving critical Sobolev exponent. With the help of Nehari manifold and the concentration‐compactness principle, we prove that problem admits at least one ground state solution. 相似文献
249.
The authors compute non-zero structure constants of the full flag manifold M = SO(7)/T with nine isotropy summands, then construct the Einstein equations. With the help of computer they get all the forty-eight positive solutions (up to a scale ) for SO(7)/T, up to isometry there are only five G-invariant Einstein metrics, of which one is Kähler Einstein metric and four are non-Kähler Einstein metrics. 相似文献
250.
In this article, we study the existence of multiple solutions for the following system driven by a nonlocal integro-differential operator with zero Dirichlet boundary conditions{(-?)_p~su = a(x)|u|~(q-2) u +2α/α + βc(x)|u|~(α-2) u|v|~β, in ?,(-?)_p~sv = b(x)|v|~(q-2) v +2β/α + βc(x)|u|α|v|~(β-2) v, in ?,u = v = 0, in Rn\?,(0.1) where Ω is a smooth bounded domain in Rn, n ps with s ∈(0,1) fixed, a(x), b(x), c(x) ≥ 0 and a(x),b(x),c(x) ∈L∞(Ω), 1 q p and α,β 1 satisfy pα + βp*,p* =np/n-ps.By Nehari manifold and fibering maps with proper conditions, we obtain the multiplicity of solutions to problem(0.1).????? 相似文献