Elliptic PDEs on Compact Ricci Limit Spaces and Applications - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Elliptic PDEs on Compact Ricci Limit Spaces and Applications write by Shouhei Honda. This book was released on 2018. Elliptic PDEs on Compact Ricci Limit Spaces and Applications available in PDF, EPUB and Kindle. In this paper we study elliptic PDEs on compact Gromov-Hausdorff limit spaces of Riemannian manifolds with lower Ricci curvature bounds. In particular we establish 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. We apply these to the study of second-order differential calculus on such limit spaces.
Elliptic PDEs on Compact Ricci Limit Spaces and Applications
Elliptic PDEs on Compact Ricci Limit Spaces and Applications - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Elliptic PDEs on Compact Ricci Limit Spaces and Applications write by Shouhei Honda. This book was released on 2018-05-29. Elliptic PDEs on Compact Ricci Limit Spaces and Applications available in PDF, EPUB and Kindle. 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.
Diophantine Approximation and the Geometry of Limit Sets in Gromov Hyperbolic Metric Spaces
Diophantine Approximation and the Geometry of Limit Sets in Gromov Hyperbolic Metric Spaces - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Diophantine Approximation and the Geometry of Limit Sets in Gromov Hyperbolic Metric Spaces write by Lior Fishman. This book was released on 2018-08-09. Diophantine Approximation and the Geometry of Limit Sets in Gromov Hyperbolic Metric Spaces available in PDF, EPUB and Kindle. 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.
Bellman Function for Extremal Problems in BMO II: Evolution
Bellman Function for Extremal Problems in BMO II: Evolution - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Bellman Function for Extremal Problems in BMO II: Evolution write by Paata Ivanisvili. This book was released on 2018-10-03. Bellman Function for Extremal Problems in BMO II: Evolution available in PDF, EPUB and Kindle. In a previous study, the authors built the Bellman function for integral functionals on the space. The present paper provides a development of the subject. They abandon the majority of unwanted restrictions on the function that generates the functional. It is the new evolutional approach that allows the authors to treat the problem in its natural setting. What is more, these new considerations lighten dynamical aspects of the Bellman function, in particular, the evolution of its picture.
On Mesoscopic Equilibrium for Linear Statistics in Dyson's Brownian Motion
On Mesoscopic Equilibrium for Linear Statistics in Dyson's Brownian Motion - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook On Mesoscopic Equilibrium for Linear Statistics in Dyson's Brownian Motion write by Maurice Duits. This book was released on 2018-10-03. On Mesoscopic Equilibrium for Linear Statistics in Dyson's Brownian Motion available in PDF, EPUB and Kindle. In this paper the authors study mesoscopic fluctuations for Dyson's Brownian motion with β=2 . Dyson showed that the Gaussian Unitary Ensemble (GUE) is the invariant measure for this stochastic evolution and conjectured that, when starting from a generic configuration of initial points, the time that is needed for the GUE statistics to become dominant depends on the scale we look at: The microscopic correlations arrive at the equilibrium regime sooner than the macrosopic correlations. The authors investigate the transition on the intermediate, i.e. mesoscopic, scales. The time scales that they consider are such that the system is already in microscopic equilibrium (sine-universality for the local correlations), but have not yet reached equilibrium at the macrosopic scale. The authors describe the transition to equilibrium on all mesoscopic scales by means of Central Limit Theorems for linear statistics with sufficiently smooth test functions. They consider two situations: deterministic initial points and randomly chosen initial points. In the random situation, they obtain a transition from the classical Central Limit Theorem for independent random variables to the one for the GUE.
