Displaying similar documents to “The discriminant and oscillation lengths for contact and Legendrian isotopies”

Isometric embeddings of a class of separable metric spaces into Banach spaces

Sophocles K. Mercourakis, Vassiliadis G. Vassiliadis (2018)

Commentationes Mathematicae Universitatis Carolinae

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Let ( M , d ) be a bounded countable metric space and c > 0 a constant, such that d ( x , y ) + d ( y , z ) - d ( x , z ) c , for any pairwise distinct points x , y , z of M . For such metric spaces we prove that they can be isometrically embedded into any Banach space containing an isomorphic copy of .

Approximately Einstein ACH metrics, volume renormalization, and an invariant for contact manifolds

Neil Seshadri (2009)

Bulletin de la Société Mathématique de France

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To any smooth compact manifold M endowed with a contact structure H and partially integrable almost CR structure J , we prove the existence and uniqueness, modulo high-order error terms and diffeomorphism action, of an approximately Einstein ACH (asymptotically complex hyperbolic) metric g on M × ( - 1 , 0 ) . We consider the asymptotic expansion, in powers of a special defining function, of the volume of M × ( - 1 , 0 ) with respect to g and prove that the log term coefficient is independent of J (and any choice...

Metric unconditionality and Fourier analysis

Stefan Neuwirth (1998)

Studia Mathematica

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We investigate several aspects of almost 1-unconditionality. We characterize the metric unconditional approximation property (umap) in terms of “block unconditionality”. Then we focus on translation invariant subspaces L E p ( ) and C E ( ) of functions on the circle and express block unconditionality as arithmetical conditions on E. Our work shows that the spaces p E ( ) , p an even integer, have a singular behaviour from the almost isometric point of view: property (umap) does not interpolate between L E p ( ) ...

Wasserstein metric and subordination

Philippe Clément, Wolfgang Desch (2008)

Studia Mathematica

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Let ( X , d X ) , ( Ω , d Ω ) be complete separable metric spaces. Denote by (X) the space of probability measures on X, by W p the p-Wasserstein metric with some p ∈ [1,∞), and by p ( X ) the space of probability measures on X with finite Wasserstein distance from any point measure. Let f : Ω p ( X ) , ω f ω , be a Borel map such that f is a contraction from ( Ω , d Ω ) into ( p ( X ) , W p ) . Let ν₁,ν₂ be probability measures on Ω with W p ( ν , ν ) finite. On X we consider the subordinated measures μ i = Ω f ω d ν i ( ω ) . Then W p ( μ , μ ) W p ( ν , ν ) . As an application we show that the solution measures ϱ α ( t ) ...

On almost everywhere differentiability of the metric projection on closed sets in l p ( n ) , 2 < p <

Tord Sjödin (2018)

Czechoslovak Mathematical Journal

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Let F be a closed subset of n and let P ( x ) denote the metric projection (closest point mapping) of x n onto F in l p -norm. A classical result of Asplund states that P is (Fréchet) differentiable almost everywhere (a.e.) in n in the Euclidean case p = 2 . We consider the case 2 < p < and prove that the i th component P i ( x ) of P ( x ) is differentiable a.e. if P i ( x ) x i and satisfies Hölder condition of order 1 / ( p - 1 ) if P i ( x ) = x i .

About w c s -covers and w c s * -networks on the Vietoris hyperspace ( X )

Luong Quoc Tuyen, Ong V. Tuyen, Phan D. Tuan, Nguzen X. Truc (2023)

Commentationes Mathematicae Universitatis Carolinae

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We study some generalized metric properties on the hyperspace ( X ) of finite subsets of a space X endowed with the Vietoris topology. We prove that X has a point-star network consisting of (countable) w c s -covers if and only if so does ( X ) . Moreover, X has a sequence of w c s -covers with property ( P ) which is a point-star network if and only if so does ( X ) , where ( P ) is one of the following properties: point-finite, point-countable, compact-finite, compact-countable, locally finite, locally countable....

On the characterization of harmonic functions with initial data in Morrey space

Bo Li, Jinxia Li, Bolin Ma, Tianjun Shen (2024)

Czechoslovak Mathematical Journal

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Let ( X , d , μ ) be a metric measure space satisfying the doubling condition and an L 2 -Poincaré inequality. Consider the nonnegative operator generalized by a Dirichlet form on X . We will show that a solution u to ( - t 2 + ) u = 0 on X × + satisfies an α -Carleson condition if and only if u can be represented as the Poisson integral of the operator with the trace in the generalized Morrey space L 2 , α ( X ) , where α is a nonnegative function defined on a class of balls in X . This result extends the analogous characterization...

Generalized Lebesgue points for Sobolev functions

Nijjwal Karak (2017)

Czechoslovak Mathematical Journal

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In many recent articles, medians have been used as a replacement of integral averages when the function fails to be locally integrable. A point x in a metric measure space ( X , d , μ ) is called a generalized Lebesgue point of a measurable function f if the medians of f over the balls B ( x , r ) converge to f ( x ) when r converges to 0 . We know that almost every point of a measurable, almost everywhere finite function is a generalized Lebesgue point and the same is true for every point of a continuous function....

Oscillatory behavior of higher order neutral differential equation with multiple functional delays under derivative operator

R.N. Rath, K.C. Panda, S.K. Rath (2022)

Archivum Mathematicum

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In this article, we obtain sufficient conditions so that every solution of neutral delay differential equation ( y ( t ) - i = 1 k p i ( t ) y ( r i ( t ) ) ) ( n ) + v ( t ) G ( y ( g ( t ) ) ) - u ( t ) H ( y ( h ( t ) ) ) = f ( t ) oscillates or tends to zero as t , where, n 1 is any positive integer, p i , r i C ( n ) ( [ 0 , ) , )  and p i are bounded for each i = 1 , 2 , , k . Further, f C ( [ 0 , ) , ) , g , h , v , u C ( [ 0 , ) , [ 0 , ) ) , G and H C ( , ) . The functional delays r i ( t ) t , g ( t ) t and h ( t ) t and all of them approach as t . The results hold when u 0 and f ( t ) 0 . This article extends, generalizes and improves some recent results, and further answers some unanswered questions from the literature. ...

Lipschitz constants for a hyperbolic type metric under Möbius transformations

Yinping Wu, Gendi Wang, Gaili Jia, Xiaohui Zhang (2024)

Czechoslovak Mathematical Journal

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Let D be a nonempty open set in a metric space ( X , d ) with D . Define h D , c ( x , y ) = log 1 + c d ( x , y ) d D ( x ) d D ( y ) , where d D ( x ) = d ( x , D ) is the distance from x to the boundary of D . For every c 2 , h D , c is a metric. We study the sharp Lipschitz constants for the metric h D , c under Möbius transformations of the unit ball, the upper half space, and the punctured unit ball.

General position properties in fiberwise geometric topology

Taras Banakh, Vesko Valov

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General position properties play a crucial role in geometric and infinite-dimensional topologies. Often such properties provide convenient tools for establishing various universality results. One of well-known general position properties is DDⁿ, the property of disjoint n-cells. Each Polish L C n - 1 -space X possessing DDⁿ contains a topological copy of each n-dimensional compact metric space. This fact implies, in particular, the classical Lefschetz-Menger-Nöbeling-Pontryagin-Tolstova embedding...

Extending generalized Whitney maps

Ivan Lončar (2017)

Archivum Mathematicum

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For metrizable continua, there exists the well-known notion of a Whitney map. If X is a nonempty, compact, and metric space, then any Whitney map for any closed subset of 2 X can be extended to a Whitney map for 2 X [3, 16.10 Theorem]. The main purpose of this paper is to prove some generalizations of this theorem.

Double weighted commutators theorem for pseudo-differential operators with smooth symbols

Yu-long Deng, Zhi-tian Chen, Shun-chao Long (2021)

Czechoslovak Mathematical Journal

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Let - ( n + 1 ) < m - ( n + 1 ) ( 1 - ρ ) and let T a ρ , δ m be pseudo-differential operators with symbols a ( x , ξ ) n × n , where 0 < ρ 1 , 0 δ < 1 and δ ρ . Let μ , λ be weights in Muckenhoupt classes A p , ν = ( μ λ - 1 ) 1 / p for some 1 < p < . We establish a two-weight inequality for commutators generated by pseudo-differential operators T a with weighted BMO functions b BMO ν , namely, the commutator [ b , T a ] is bounded from L p ( μ ) into L p ( λ ) . Furthermore, the range of m can be extended to the whole m - ( n + 1 ) ( 1 - ρ ) .