Due 2018-02-28
1st ed. 2018, X, 175 p. 3illus., 2 illus. in color.
Hardcover
ISBN 978-3-319-73125-4
Includes contributions from leading international researchers in the area
Offers a survey of challenging open problems in this field
Provides deep insights into new connections between different areas of research
The book collects the most relevant outcomes from the INdAM Workshop “Geometric Function
Theory in Higher Dimension” held in Cortona on September 5-9, 2016.
The Workshop was mainly devoted to discussions of basic open problems in the area, and this volume follows the
same line. In particular, it offers a selection of original contributions on Loewner theory in one
and higher dimensions, semigroups theory, iteration theory and related topics.
Written by experts in geometric function theory in one and several complex variables, it focuses on new
research frontiers in this area and on challenging open problems. The book is intended for
graduate students and researchers working in complex analysis, several complex variables and
geometric function theory.
Due 2018-03-08
1st ed. 2018, Approx. 600 p.2 illus. in color.
Hardcover
ISBN 978-3-319-73289-3
Presents Harish-Chandra’s unpublished material involving real groups
Focuses exclusively on the theorems which Harish-Chandra had announced without proofs
Brings out the unpublished material in a more coherent form than the set of
manuscripts to be found in the Archives at the Institute for Advanced Study, Princeton, NJ, USA
This volume is to be regarded as the fifth in the series of Harish-Chandra’s collected papers,
continuing the four volumes already published by Springer-Verlag. Because of manifold
illnesses in the last ten years of his life, a large part of Harish-Chandra’s work remained
unpublished. The present volume deals with those unpublished manuscripts involving real
groups, and includes only those pertaining to the theorems which Harish-Chandra had
announced without proofs. An attempt has been made by the volume editors to bring out this
material in a more coherent form than in the handwritten manuscripts, although nothing
essentially new has been added and editorial comments are kept to a minimum. The papers
deal with several topics: characters on non-connected real groups, Fourier transforms of orbital
integrals, Whittaker theory, and supertempered characters. The generality of Harish-Chandra’s
results in these papers far exceeds anything in print. The volume will be of great interest to all
mathematicians interested in Lie groups, and all who have an interest in the opus of a
twentieth century giant. Harish-Chandra was a great mathematician, perhaps one of the
greatest of the second half of the twentieth century.
Due 2018-06-22
1st ed. 2018, Approx. 450 p.
Softcover
ISBN 978-3-319-70868-3
Series Advanced Courses in Mathematics - CRM Barcelona
Provides a solid introduction to the theory of topological dynamics and
crossed products
Contains a large collection of examples and explicit computations
Shows developments in topological orbit equivalence, particularly treating the
classification of minimal actions of finitely generated abelian groups on the
Cantor set
This book collects the notes of the lectures given at an Advanced Course on Dynamical
Systems at the Centre de Recerca Matematica (CRM) in Barcelona. The notes consist of four
series of lectures. The first one, given by Andrew Toms, presents the basic properties of the
Cuntz semigroup and its role in the classification program of simple, nuclear, separable C*-
algebras. The second series of lectures, delivered by N. Christopher Phillips, serves as an
introduction to group actions on C*-algebras and their crossed products, with emphasis on the
simple case and when the said products are classifiable. The third one, given by David Kerr,
treats various developments related to measure-theoretic and topological aspects of crossed
products, focusing on internal and external approximation concepts, both for groups and C*-
algebras. Finally, the last series of lectures, delivered by Thierry Giordano, is devoted to the
theory of topological orbit equivalence, with particular attention to the classification of minimal
actions by finitely generated abelian groups on the Cantor set.
Nankai Tracts in Mathematics
380pp Aug 2018
ISBN: 978-981-3236-05-9 (hardcover)
In the theory of minimal submanifolds, Bernstein's problem and Plateau's problem are central topics. This important book presents the Douglas?Rado solution to Plateau's problem, but the main emphasis is on Bernstein's problem and its new developments in various directions: the value distribution of the Gauss image of a minimal surface in Euclidean 3-space, Simons' work for minimal graphic hypersurfaces, and the author's own contributions to Bernstein type theorems for higher codimension. The author also introduces some related topics, such as submanifolds with parallel mean curvature, Weierstrass type representation for surfaces of mean curvature 1 in hyperbolic 3-space, and special Lagrangian submanifolds.
This new edition contains the author's recent work on the Lawson?Osseman's problem for higher codimension, and on Chern's problem for minimal hypersurfaces in the sphere. Both Chern's problem and Lawson?Osserman's problem are important problems in minimal surface theory which are still unsolved. In addition, some new techniques were developed to address those problems in detail, which are of interest in the field of geometric analysis.
Introduction
Bernstein's Theorem and Its Generalizations
Weistrass Type Representations
Plateau's Problem and Douglas?Rado Solution
Intrinsic Rigidity Theorems
Stable Minimal Hypersurfaces
Minimal Submanifolds of Higher Codimension
Bernstein Type Theorems for Higher Codimension
Entire Space-Like Submanifold
Researchers and graduate students in differential geometry.