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881.
Wayne Rossman 《Journal of Geometric Analysis》2001,11(4):669-692
We describe local similarities and global differences between minimal surfaces in Euclidean 3-space and constant mean curvature
1 surfaces in hyperbolic 3-space. We also describe how to solve global period problems for constant mean curvature 1 surfaces
in hyperbolic 3-space, and we give an overview of recent results on these surfaces. We include computer graphics of a number
of examples. 相似文献
882.
We deal with variational problems on varying manifolds in ℝn. We represent each manifold by a positive measure μ, to which we associate a suitable notion of tangent space Tμ, of mean
curvature H(μ), and of Sobolev spaces with respect to μ on an open subset Ω ⊆ ℝn. We introduce the notions of weak and strong convergence for functions defined on varying manifolds, that is defined μh -a.e., being {μh} a weakly convergent sequence of measures. In this setting, we prove a strong-weak type compactness theorem for the pairs
(Pμ
h H(μh)), where Pμ
h are the projectors onto the tangent spaces Tμ
h. When μh belong to a suitable class of k-dimensional measures, having in particular a prescribed (k−1)-manifold as a boundary, we
enforce this result to study the convergence of energy functionals, possibly with a Dirichlet condition on ∂Ω. We also address
a perspective for optimization problems where the control variable is represented by a manifold with a prescribed boundary. 相似文献
883.
In recent papers the authors presented their approach to Feynman’s operational calculi for a system of not necessarily commuting
bounded linear operators acting on a Banach space. The central objects of the theory are the disentangling algebra, a commutative
Banach algebra, and the disentangling map which carries this commutative structure into the noncommutative algebra of operators.
Under assumptions concerning the growth of disentangled exponential expressions, the associated functional calculus for the
system of operators is a distribution with compact support which we view as the joint spectrum of the operators with respect
to the disentangling map. In this paper, the functional calculus is represented in terms of a higher-dimensional analogue
of the Riesz-Dunford calculus using Clifford analysis. 相似文献
884.
Let be a hypergraph. A panchromatic t-colouring of is a t-colouring of its vertices such that each edge has at least one vertex of each colour; and is panchromatically t-choosable if, whenever each vertex is given a list of t colours, the vertices can be coloured from their lists in such a way that each edge receives at least t different colours. The Hall ratio of is . Among other results, it is proved here that if every edge has at least t vertices and whenever , then is panchromatically t-choosable, and this condition is sharp; the minimum such that every t-uniform hypergraph with is panchromatically t-choosable satisfies ; and except possibly when t = 3 or 5, a t-uniform hypergraph is panchromatically t-colourable if whenever , and this condition is sharp. This last result dualizes to a sharp sufficient condition for the chromatic index of a hypergraph
to equal its maximum degree.
Received November 10, 1998
RID="*"
ID="*" This work was carried out while the first author was visiting Nottingham, funded by Visiting Fellowship Research Grant
GR/L54585 from the Engineering and Physical Sciences Research Council. The work of this author was also partly supported by
grants 96-01-01614 and 97-01-01075 of the Russian Foundation for Fundamental Research. 相似文献
885.
In this paper we develop a theory of parabolic pseudodifferential operators in anisotropic spaces. We construct a symbolic calculus for a class of symbols globally defined on
n+1×
n+1, and then develop a periodisation procedure for the calculus of symbols on the cylinder
×. We show Gårding's inequality for suitable operators and precise estimates for the essential norm in anisotropic Sobolev spaces. These new mapping properties are needed in localization arguments for the analysis of numerical approximation methods. 相似文献
886.
Rene L. Schilling 《Integral Equations and Operator Theory》2001,41(1):74-92
Let (A, D(A)) denote the infinitesimal generator of some strongly continuous sub-Markovian contraction semigroup onL
p
(m), p1 andm not necessarily -finite. We show under mild regularity conditions thatA is a Dirichlet operator in all spacesL
q
(m), qp. It turns out that, in the limitq,A satisfies the positive maximum principle. If the test functionsC
c
D(A), then the positive maximum principle implies thatA is a pseudo-differential operator associated with a negative definite symbol, i.e., a Lévy-type operator. Conversely, we provide sufficient criteria for an operator (A, D(A)) onL
p(m) satisfying the positive maximum principle to be a Dirichlet operator. If, in particular,A onL
2
(m) is a symmetric integro-differential operator associated with a negative definite symbol, thenA extends to a generator of a regular (symmetric) Dirichlet form onL
2
(m) with explicitly given Beurling-Deny formula. 相似文献
887.
In this paper we show that the weakly -Engel conditions are closely related to the existance of normal -complements; while the -Engel conditions are closely related to the -nilpotent groups.AMS Subject Classification (2000): 20D20 相似文献
888.
Given H≥0 and bounded convex curves α1, ...,⇌n, α in the plane z=0 bounding domains D1, …, Dn, D, respectively, with
if i ∈ j and with Di ⊂ D, we obtain several results proving the existence of a constanth depending only on H and on the geometry of the curves
αi, α such that the Dirichlet problem for the constant mean curvature H equation:
where
may accept or not a solution. 相似文献
889.
Silvano Delladio 《Journal of Geometric Analysis》2001,11(1):17-42
We show that the L
p
norm of the second fundamental form of hypersurfaces in
R
n+1
is very coercive in the GMT setting of Gauss graphs currents, when p exceeds the dimension n. A compactness result for immersed
hypersurfaces and its application to a variational problem are provided. 相似文献
890.
László Zsilinszky 《Rendiconti del Circolo Matematico di Palermo》2000,49(2):371-380
This is a continuation of [19]. We characterize first and second countability of the general hit-and-miss hyperspace topologyτ
+
Δ
for weakly-R
0 base spaces. Further, metrizability ofτ
+
Δ
is characterized with no preliminary conditions on the base space and the generating family of closed sets and a new proof
on uniformizability (i.e. complete regularity) ofτ
+
Δ
is given in this general setting, thus generalizing results of [3], [5] and [6]. 相似文献