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Titlebook: Holomorphic Curves and Global Questions in Contact Geometry; Casim Abbas,Helmut Hofer Textbook 2019 Springer Nature Switzerland AG 2019 fi

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发表于 2025-3-21 17:36:02 | 显示全部楼层 |阅读模式
书目名称Holomorphic Curves and Global Questions in Contact Geometry
编辑Casim Abbas,Helmut Hofer
视频video
概述Entry point to Symplectic Field Theory (SFT).Entry point for the study of finite energy foliations.Proves deep results in pseudoholomorphic curve theory.Written by leading researchers in this area.A m
丛书名称Birkhäuser Advanced Texts‘ Basler Lehrbücher
图书封面Titlebook: Holomorphic Curves and Global Questions in Contact Geometry;  Casim Abbas,Helmut Hofer Textbook 2019 Springer Nature Switzerland AG 2019 fi
描述.This book explains the foundations of holomorphic curve theory in contact geometry. By using a particular geometric problem as a starting point the authors guide the reader into the subject. As such it ideally serves as preparation and as entry point for a deeper study of the analysis underlying symplectic field theory..An introductory chapter sets the stage explaining some of the basic notions of contact geometry and the role of holomorphic curves in the field. The authors proceed to the heart of the material providing a detailed exposition about finite energy planes and periodic orbits (chapter 4) to disk filling methods and applications (chapter 9)..The material is self-contained. It includes a number of technical appendices giving the geometric analysis foundations for the main results, so that one may easily follow the discussion. Graduate students as well as researchers who want to learn the basics of this fast developing theory will highly appreciate this accessible approach taken by the authors..
出版日期Textbook 2019
关键词finite energy planes; weinstein conjecture; pseudoholomorphic curves; disk filling method; contact forms
版次1
doihttps://doi.org/10.1007/978-3-030-11803-7
isbn_ebook978-3-030-11803-7Series ISSN 1019-6242 Series E-ISSN 2296-4894
issn_series 1019-6242
copyrightSpringer Nature Switzerland AG 2019
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An Introduction to Contact Geometry,A . on an odd-dimensional manifold . of dimension 2. + 1 is a one-form . such that the (2. + 1)-form Ω given by . defines a volume form on .. We observe that any manifold admitting a contact form is necessarily orientable, and that a contact form defines a natural orientation.
发表于 2025-3-22 06:11:09 | 显示全部楼层
Finite Energy Planes and Periodic Orbits,In this chapter we will prove the main result on finite energy planes due to H. Hofer [.] (see also [.]). Namely, given any manifold . equipped with a contact form ., denote by . → . the associated contact structure and by .. the associated Reeb vector field.
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Disk Filling Methods and Applications,Let (., .) be a closed three dimensional contact manifold with overtwisted contact structure .. Then there exists a contractible periodic orbit for the Reeb vector field ...
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