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Author: Stefano Bianchini
Publisher:
Published: 2018
Total Pages:
ISBN-13: 9781470442781
DOWNLOAD EBOOKDownload or read book On Sudakov's Type Decomposition of Transference Plans with Norm Costs written by Stefano Bianchini and published by . This book was released on 2018 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author: Stefano Bianchini
Publisher: American Mathematical Soc.
Published: 2018-02-23
Total Pages: 112
ISBN-13: 1470427664
DOWNLOAD EBOOKThe authors consider the original strategy proposed by Sudakov for solving the Monge transportation problem with norm cost with , probability measures in and absolutely continuous w.r.t. . The key idea in this approach is to decompose (via disintegration of measures) the Kantorovich optimal transportation problem into a family of transportation problems in , where are disjoint regions such that the construction of an optimal map is simpler than in the original problem, and then to obtain by piecing together the maps . When the norm is strictly convex, the sets are a family of -dimensional segments determined by the Kantorovich potential called optimal rays, while the existence of the map is straightforward provided one can show that the disintegration of (and thus of ) on such segments is absolutely continuous w.r.t. the -dimensional Hausdorff measure. When the norm is not strictly convex, the main problems in this kind of approach are two: first, to identify a suitable family of regions on which the transport problem decomposes into simpler ones, and then to prove the existence of optimal maps. In this paper the authors show how these difficulties can be overcome, and that the original idea of Sudakov can be successfully implemented. The results yield a complete characterization of the Kantorovich optimal transportation problem, whose straightforward corollary is the solution of the Monge problem in each set and then in . The strategy is sufficiently powerful to be applied to other optimal transportation problems.
Download or read book On Sudakov’s Type Decomposition of Transference Plans with Norm Costs written by Stefano Bianchini and published by American Mathematical Soc.. This book was released on 2018-02-23 with total page 112 pages. Available in PDF, EPUB and Kindle. Book excerpt: The authors consider the original strategy proposed by Sudakov for solving the Monge transportation problem with norm cost with , probability measures in and absolutely continuous w.r.t. . The key idea in this approach is to decompose (via disintegration of measures) the Kantorovich optimal transportation problem into a family of transportation problems in , where are disjoint regions such that the construction of an optimal map is simpler than in the original problem, and then to obtain by piecing together the maps . When the norm is strictly convex, the sets are a family of -dimensional segments determined by the Kantorovich potential called optimal rays, while the existence of the map is straightforward provided one can show that the disintegration of (and thus of ) on such segments is absolutely continuous w.r.t. the -dimensional Hausdorff measure. When the norm is not strictly convex, the main problems in this kind of approach are two: first, to identify a suitable family of regions on which the transport problem decomposes into simpler ones, and then to prove the existence of optimal maps. In this paper the authors show how these difficulties can be overcome, and that the original idea of Sudakov can be successfully implemented. The results yield a complete characterization of the Kantorovich optimal transportation problem, whose straightforward corollary is the solution of the Monge problem in each set and then in . The strategy is sufficiently powerful to be applied to other optimal transportation problems.
Author: Alastair J. Litterick
Publisher: American Mathematical Soc.
Published: 2018-05-29
Total Pages: 156
ISBN-13: 1470428377
DOWNLOAD EBOOKDownload or read book On Non-Generic Finite Subgroups of Exceptional Algebraic Groups written by Alastair J. Litterick and published by American Mathematical Soc.. This book was released on 2018-05-29 with total page 156 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author: Chin-Yu Hsiao
Publisher: American Mathematical Soc.
Published: 2018-08-09
Total Pages: 140
ISBN-13: 1470441012
DOWNLOAD EBOOKLet X be an abstract not necessarily compact orientable CR manifold of dimension 2n−1, n⩾2, and let Lk be the k-th tensor power of a CR complex line bundle L over X. Given q∈{0,1,…,n−1}, let □(q)b,k be the Gaffney extension of Kohn Laplacian for (0,q) forms with values in Lk. For λ≥0, let Π(q)k,≤λ:=E((−∞,λ]), where E denotes the spectral measure of □(q)b,k. In this work, the author proves that Π(q)k,≤k−N0F∗k, FkΠ(q)k,≤k−N0F∗k, N0≥1, admit asymptotic expansions with respect to k on the non-degenerate part of the characteristic manifold of □(q)b,k, where Fk is some kind of microlocal cut-off function. Moreover, we show that FkΠ(q)k,≤0F∗k admits a full asymptotic expansion with respect to k if □(q)b,k has small spectral gap property with respect to Fk and Π(q)k,≤0 is k-negligible away the diagonal with respect to Fk. By using these asymptotics, the authors establish almost Kodaira embedding theorems on CR manifolds and Kodaira embedding theorems on CR manifolds with transversal CR S1 action.
Download or read book Szegő Kernel Asymptotics for High Power of CR Line Bundles and Kodaira Embedding Theorems on CR Manifolds written by Chin-Yu Hsiao and published by American Mathematical Soc.. This book was released on 2018-08-09 with total page 140 pages. Available in PDF, EPUB and Kindle. Book excerpt: Let X be an abstract not necessarily compact orientable CR manifold of dimension 2n−1, n⩾2, and let Lk be the k-th tensor power of a CR complex line bundle L over X. Given q∈{0,1,…,n−1}, let □(q)b,k be the Gaffney extension of Kohn Laplacian for (0,q) forms with values in Lk. For λ≥0, let Π(q)k,≤λ:=E((−∞,λ]), where E denotes the spectral measure of □(q)b,k. In this work, the author proves that Π(q)k,≤k−N0F∗k, FkΠ(q)k,≤k−N0F∗k, N0≥1, admit asymptotic expansions with respect to k on the non-degenerate part of the characteristic manifold of □(q)b,k, where Fk is some kind of microlocal cut-off function. Moreover, we show that FkΠ(q)k,≤0F∗k admits a full asymptotic expansion with respect to k if □(q)b,k has small spectral gap property with respect to Fk and Π(q)k,≤0 is k-negligible away the diagonal with respect to Fk. By using these asymptotics, the authors establish almost Kodaira embedding theorems on CR manifolds and Kodaira embedding theorems on CR manifolds with transversal CR S1 action.
Author: Roelof Bruggeman
Publisher: American Mathematical Soc.
Published: 2018-05-29
Total Pages: 167
ISBN-13: 1470428555
DOWNLOAD EBOOKDownload or read book Holomorphic Automorphic Forms and Cohomology written by Roelof Bruggeman and published by American Mathematical Soc.. This book was released on 2018-05-29 with total page 167 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author: Shouhei Honda
Publisher: American Mathematical Soc.
Published: 2018-05-29
Total Pages: 92
ISBN-13: 1470428547
DOWNLOAD EBOOKIn this paper the author studies elliptic PDEs on compact Gromov-Hausdorff limit spaces of Riemannian manifolds with lower Ricci curvature bounds. In particular the author establishes continuities of geometric quantities, which include solutions of Poisson's equations, eigenvalues of Schrödinger operators, generalized Yamabe constants and eigenvalues of the Hodge Laplacian, with respect to the Gromov-Hausdorff topology. The author applies these to the study of second-order differential calculus on such limit spaces.
Download or read book Elliptic PDEs on Compact Ricci Limit Spaces and Applications written by Shouhei Honda and published by American Mathematical Soc.. This book was released on 2018-05-29 with total page 92 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this paper the author studies elliptic PDEs on compact Gromov-Hausdorff limit spaces of Riemannian manifolds with lower Ricci curvature bounds. In particular the author establishes continuities of geometric quantities, which include solutions of Poisson's equations, eigenvalues of Schrödinger operators, generalized Yamabe constants and eigenvalues of the Hodge Laplacian, with respect to the Gromov-Hausdorff topology. The author applies these to the study of second-order differential calculus on such limit spaces.
Author: Anne-Laure Dalibard
Publisher: American Mathematical Soc.
Published: 2018-05-29
Total Pages: 111
ISBN-13: 1470428350
DOWNLOAD EBOOKDownload or read book Mathematical Study of Degenerate Boundary Layers: A Large Scale Ocean Circulation Problem written by Anne-Laure Dalibard and published by American Mathematical Soc.. This book was released on 2018-05-29 with total page 111 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author: Cristian Anghel
Publisher: American Mathematical Soc.
Published: 2018-05-29
Total Pages: 107
ISBN-13: 1470428385
DOWNLOAD EBOOKDownload or read book Globally Generated Vector Bundles with Small C1 on Projective Spaces written by Cristian Anghel and published by American Mathematical Soc.. This book was released on 2018-05-29 with total page 107 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author: Sebastiano Carpi
Publisher: American Mathematical Soc.
Published: 2018-08-09
Total Pages: 85
ISBN-13: 147042858X
DOWNLOAD EBOOKThe authors consider unitary simple vertex operator algebras whose vertex operators satisfy certain energy bounds and a strong form of locality and call them strongly local. They present a general procedure which associates to every strongly local vertex operator algebra V a conformal net AV acting on the Hilbert space completion of V and prove that the isomorphism class of AV does not depend on the choice of the scalar product on V. They show that the class of strongly local vertex operator algebras is closed under taking tensor products and unitary subalgebras and that, for every strongly local vertex operator algebra V, the map W↦AW gives a one-to-one correspondence between the unitary subalgebras W of V and the covariant subnets of AV.
Download or read book From Vertex Operator Algebras to Conformal Nets and Back written by Sebastiano Carpi and published by American Mathematical Soc.. This book was released on 2018-08-09 with total page 85 pages. Available in PDF, EPUB and Kindle. Book excerpt: The authors consider unitary simple vertex operator algebras whose vertex operators satisfy certain energy bounds and a strong form of locality and call them strongly local. They present a general procedure which associates to every strongly local vertex operator algebra V a conformal net AV acting on the Hilbert space completion of V and prove that the isomorphism class of AV does not depend on the choice of the scalar product on V. They show that the class of strongly local vertex operator algebras is closed under taking tensor products and unitary subalgebras and that, for every strongly local vertex operator algebra V, the map W↦AW gives a one-to-one correspondence between the unitary subalgebras W of V and the covariant subnets of AV.
Author: Zhou Gang
Publisher: American Mathematical Soc.
Published: 2018-05-29
Total Pages: 78
ISBN-13: 1470428407
DOWNLOAD EBOOKDownload or read book Neckpinch Dynamics for Asymmetric Surfaces Evolving by Mean Curvature Flow written by Zhou Gang and published by American Mathematical Soc.. This book was released on 2018-05-29 with total page 78 pages. Available in PDF, EPUB and Kindle. Book excerpt:
