Dynamical Zeta Functions, Nielsen Theory and Reidemeister Torsion
Dynamical Zeta Functions, Nielsen Theory and Reidemeister Torsion

Author: Alexander Fel'shtyn

Publisher: American Mathematical Soc.

Published: 2000

Total Pages: 165

ISBN-13: 0821820907

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In the paper we study new dynamical zeta functions connected with Nielsen fixed point theory. The study of dynamical zeta functions is part of the theory of dynamical systems, but it is also intimately related to algebraic geometry, number theory, topology and statistical mechanics. The paper consists of four parts. Part I presents a brief account of the Nielsen fixed point theory. Part II deals with dynamical zeta functions connected with Nielsen fixed point theory. Part III is concerned with analog of Dold congruences for the Reidemeister and Nielsen numbers. In Part IV we explain how dynamical zeta functions give rise to the Reidemeister torsion, a very important topological invariant which has useful applications in knots theory,quantum field theory and dynamical systems.

Geometry and Analysis on Complex Manifolds
Geometry and Analysis on Complex Manifolds

Author: Toshiki Mabuchi

Publisher: World Scientific

Published: 1994

Total Pages: 268

ISBN-13: 9789810220679

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This volume presents papers dedicated to Professor Shoshichi Kobayashi, commemorating the occasion of his sixtieth birthday on January 4, 1992.The principal theme of this volume is “Geometry and Analysis on Complex Manifolds”. It emphasizes the wide mathematical influence that Professor Kobayashi has on areas ranging from differential geometry to complex analysis and algebraic geometry. It covers various materials including holomorphic vector bundles on complex manifolds, Kähler metrics and Einstein–Hermitian metrics, geometric function theory in several complex variables, and symplectic or non-Kähler geometry on complex manifolds. These are areas in which Professor Kobayashi has made strong impact and is continuing to make many deep invaluable contributions.

Value Distribution Theory of the Gauss Map of Minimal Surfaces in Rm
Value Distribution Theory of the Gauss Map of Minimal Surfaces in Rm

Author: Hirotaka Fujimoto

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 222

ISBN-13: 332280271X

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This book presents in a systematic and almost self-contained way the striking analogy between classical function theory, in particular the value distribution theory of holomorphic curves in projective space, on the one hand, and important and beautiful properties of the Gauss map of minimal surfaces on the other hand. Both theories are developed in the text, including many results of recent research. The relations and analogies between them become completely clear. The book is written for interested graduate students and mathematicians, who want to become more familiar with this modern development in the two classical areas of mathematics, but also for those, who intend to do further research on minimal surfaces.

Geometry And Analysis On Complex Manifolds: Festschrift For S Kobayashi's 60th Birthday
Geometry And Analysis On Complex Manifolds: Festschrift For S Kobayashi's 60th Birthday

Author: Toshiki Mabuchi

Publisher: World Scientific

Published: 1994-12-09

Total Pages: 261

ISBN-13: 9814501220

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This volume presents papers dedicated to Professor Shoshichi Kobayashi, commemorating the occasion of his sixtieth birthday on January 4, 1992.The principal theme of this volume is “Geometry and Analysis on Complex Manifolds”. It emphasizes the wide mathematical influence that Professor Kobayashi has on areas ranging from differential geometry to complex analysis and algebraic geometry. It covers various materials including holomorphic vector bundles on complex manifolds, Kähler metrics and Einstein-Hermitian metrics, geometric function theory in several complex variables, and symplectic or non-Kähler geometry on complex manifolds. These are areas in which Professor Kobayashi has made strong impact and is continuing to make many deep invaluable contributions.

Renormalized Self-Intersection Local Times and Wick Power Chaos Processes
Renormalized Self-Intersection Local Times and Wick Power Chaos Processes

Author: Michael B. Marcus

Publisher: American Mathematical Soc.

Published: 1999

Total Pages: 138

ISBN-13: 0821813404

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Sufficient conditions are obtained for the continuity of renormalized self-intersection local times for the multiple intersections of a large class of strongly symmetric L vy processes in $R DEGREESm$, $m=1,2$. In $R DEGREES2$ these include Brownian motion and stable processes of index greater than 3/2, as well as many processes in their domains of attraction. In $R DEGREES1$ these include stable processes of index $3/4