The Planar Cubic Cayley Graphs
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The Planar Cubic Cayley Graphs
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Author : Agelos Georgakopoulos
language : en
Publisher: American Mathematical Soc.
Release Date : 2018-01-16
The Planar Cubic Cayley Graphs written by Agelos Georgakopoulos and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-01-16 with Mathematics categories.
The author obtains a complete description of the planar cubic Cayley graphs, providing an explicit presentation and embedding for each of them. This turns out to be a rich class, comprising several infinite families. He obtains counterexamples to conjectures of Mohar, Bonnington and Watkins. The author's analysis makes the involved graphs accessible to computation, corroborating a conjecture of Droms.
Szego Kernel Asymptotics For High Power Of Cr Line Bundles And Kodaira Embedding Theorems On Cr Manifolds
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Author : Chin-Yu Hsiao
language : en
Publisher: American Mathematical Soc.
Release Date : 2018-08-09
Szego Kernel Asymptotics For High Power Of Cr Line Bundles And Kodaira Embedding Theorems On Cr Manifolds written by Chin-Yu Hsiao and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-08-09 with Mathematics categories.
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.
Mathematical Study Of Degenerate Boundary Layers A Large Scale Ocean Circulation Problem
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Author : Anne-Laure Dalibard
language : en
Publisher: American Mathematical Soc.
Release Date : 2018-05-29
Mathematical Study Of Degenerate Boundary Layers A Large Scale Ocean Circulation Problem written by Anne-Laure Dalibard and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-05-29 with Mathematics categories.
This paper is concerned with a complete asymptotic analysis as $E \to 0$ of the Munk equation $\partial _x\psi -E \Delta ^2 \psi = \tau $ in a domain $\Omega \subset \mathbf R^2$, supplemented with boundary conditions for $\psi $ and $\partial _n \psi $. This equation is a simple model for the circulation of currents in closed basins, the variables $x$ and $y$ being respectively the longitude and the latitude. A crude analysis shows that as $E \to 0$, the weak limit of $\psi $ satisfies the so-called Sverdrup transport equation inside the domain, namely $\partial _x \psi ^0=\tau $, while boundary layers appear in the vicinity of the boundary.
Bordered Heegaard Floer Homology
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Author : Robert Lipshitz
language : en
Publisher: American Mathematical Soc.
Release Date : 2018-08-09
Bordered Heegaard Floer Homology written by Robert Lipshitz and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-08-09 with Mathematics categories.
The authors construct Heegaard Floer theory for 3-manifolds with connected boundary. The theory associates to an oriented, parametrized two-manifold a differential graded algebra. For a three-manifold with parametrized boundary, the invariant comes in two different versions, one of which (type D) is a module over the algebra and the other of which (type A) is an A∞ module. Both are well-defined up to chain homotopy equivalence. For a decomposition of a 3-manifold into two pieces, the A∞ tensor product of the type D module of one piece and the type A module from the other piece is ^HF of the glued manifold. As a special case of the construction, the authors specialize to the case of three-manifolds with torus boundary. This case can be used to give another proof of the surgery exact triangle for ^HF. The authors relate the bordered Floer homology of a three-manifold with torus boundary with the knot Floer homology of a filling.
Perihelia Reduction And Global Kolmogorov Tori In The Planetary Problem
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Author : Gabriella Pinzari
language : en
Publisher: American Mathematical Soc.
Release Date : 2018-10-03
Perihelia Reduction And Global Kolmogorov Tori In The Planetary Problem written by Gabriella Pinzari and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-10-03 with Mathematics categories.
The author proves the existence of an almost full measure set of -dimensional quasi-periodic motions in the planetary problem with masses, with eccentricities arbitrarily close to the Levi–Civita limiting value and relatively high inclinations. This extends previous results, where smallness of eccentricities and inclinations was assumed. The question had been previously considered by V. I. Arnold in the 1960s, for the particular case of the planar three-body problem, where, due to the limited number of degrees of freedom, it was enough to use the invariance of the system by the SO(3) group. The proof exploits nice parity properties of a new set of coordinates for the planetary problem, which reduces completely the number of degrees of freedom for the system (in particular, its degeneracy due to rotations) and, moreover, is well fitted to its reflection invariance. It allows the explicit construction of an associated close to be integrable system, replacing Birkhoff normal form, a common tool of previous literature.
Elliptic Pdes On Compact Ricci Limit Spaces And Applications
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Author : Shouhei Honda
language : en
Publisher: American Mathematical Soc.
Release Date : 2018-05-29
Elliptic Pdes On Compact Ricci Limit Spaces And Applications written by Shouhei Honda and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-05-29 with Mathematics categories.
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.
A Morse Bott Approach To Monopole Floer Homology And The Triangulation Conjecture
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Author : Francesco Lin
language : en
Publisher: American Mathematical Soc.
Release Date : 2018-10-03
A Morse Bott Approach To Monopole Floer Homology And The Triangulation Conjecture written by Francesco Lin and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-10-03 with Mathematics categories.
In the present work the author generalizes the construction of monopole Floer homology due to Kronheimer and Mrowka to the case of a gradient flow with Morse-Bott singularities. Focusing then on the special case of a three-manifold equipped equipped with a structure which is isomorphic to its conjugate, the author defines the counterpart in this context of Manolescu's recent Pin(2)-equivariant Seiberg-Witten-Floer homology. In particular, the author provides an alternative approach to his disproof of the celebrated Triangulation conjecture.
Globally Generated Vector Bundles With Small C 1 On Projective Spaces
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Author : Cristian Anghel
language : en
Publisher: American Mathematical Soc.
Release Date : 2018-05-29
Globally Generated Vector Bundles With Small C 1 On Projective Spaces written by Cristian Anghel and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-05-29 with Mathematics categories.
The authors provide a complete classification of globally generated vector bundles with first Chern class $c_1 \leq 5$ one the projective plane and with $c_1 \leq 4$ on the projective $n$-space for $n \geq 3$. This reproves and extends, in a systematic manner, previous results obtained for $c_1 \leq 2$ by Sierra and Ugaglia [J. Pure Appl. Algebra 213 (2009), 2141-2146], and for $c_1 = 3$ by Anghel and Manolache [Math. Nachr. 286 (2013), 1407-1423] and, independently, by Sierra and Ugaglia [J. Pure Appl. Algebra 218 (2014), 174-180]. It turns out that the case $c_1 = 4$ is much more involved than the previous cases, especially on the projective 3-space. Among the bundles appearing in our classification one can find the Sasakura rank 3 vector bundle on the projective 4-space (conveniently twisted). The authors also propose a conjecture concerning the classification of globally generated vector bundles with $c_1 \leq n - 1$ on the projective $n$-space. They verify the conjecture for $n \leq 5$.
Holomorphic Automorphic Forms And Cohomology
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Author : Roelof Bruggeman
language : en
Publisher: American Mathematical Soc.
Release Date : 2018-05-29
Holomorphic Automorphic Forms And Cohomology written by Roelof Bruggeman and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-05-29 with Mathematics categories.
Diophantine Approximation And The Geometry Of Limit Sets In Gromov Hyperbolic Metric Spaces
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Author : Lior Fishman
language : en
Publisher: American Mathematical Soc.
Release Date : 2018-08-09
Diophantine Approximation And The Geometry Of Limit Sets In Gromov Hyperbolic Metric Spaces written by Lior Fishman and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-08-09 with Mathematics categories.
In this paper, the authors provide a complete theory of Diophantine approximation in the limit set of a group acting on a Gromov hyperbolic metric space. This summarizes and completes a long line of results by many authors, from Patterson's classic 1976 paper to more recent results of Hersonsky and Paulin (2002, 2004, 2007). The authors consider concrete examples of situations which have not been considered before. These include geometrically infinite Kleinian groups, geometrically finite Kleinian groups where the approximating point is not a fixed point of any element of the group, and groups acting on infinite-dimensional hyperbolic space. Moreover, in addition to providing much greater generality than any prior work of which the authors are aware, the results also give new insight into the nature of the connection between Diophantine approximation and the geometry of the limit set within which it takes place. Two results are also contained here which are purely geometric: a generalization of a theorem of Bishop and Jones (1997) to Gromov hyperbolic metric spaces, and a proof that the uniformly radial limit set of a group acting on a proper geodesic Gromov hyperbolic metric space has zero Patterson–Sullivan measure unless the group is quasiconvex-cocompact. The latter is an application of a Diophantine theorem.