A survey on classical minimal surface theory
著者
書誌事項
A survey on classical minimal surface theory
(University lecture series, v. 60)
American Mathematical Society, c2012
大学図書館所蔵 全34件
  青森
  岩手
  宮城
  秋田
  山形
  福島
  茨城
  栃木
  群馬
  埼玉
  千葉
  東京
  神奈川
  新潟
  富山
  石川
  福井
  山梨
  長野
  岐阜
  静岡
  愛知
  三重
  滋賀
  京都
  大阪
  兵庫
  奈良
  和歌山
  鳥取
  島根
  岡山
  広島
  山口
  徳島
  香川
  愛媛
  高知
  福岡
  佐賀
  長崎
  熊本
  大分
  宮崎
  鹿児島
  沖縄
  韓国
  中国
  タイ
  イギリス
  ドイツ
  スイス
  フランス
  ベルギー
  オランダ
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  アメリカ
注記
Includes bibliographical references (p. 171-182)
内容説明・目次
内容説明
Meeks and Perez present a survey of recent spectacular successes in classical minimal surface theory. The classification of minimal planar domains in three-dimensional Euclidean space provides the focus of the account. The proof of the classification depends on the work of many currently active leading mathematicians, thus making contact with much of the most important results in the field. Through the telling of the story of the classification of minimal planar domains, the general mathematician may catch a glimpse of the intrinsic beauty of this theory and the authors' perspective of what is happening at this historical moment in a very classical subject. This book includes an updated tour through some of the recent advances in the theory, such as Colding-Minicozzi theory, minimal laminations, the ordering theorem for the space of ends, conformal structure of minimal surfaces, minimal annular ends with infinite total curvature, the embedded Calabi-Yau problem, local pictures on the scale of curvature and topology, the local removable singularity theorem, embedded minimal surfaces of finite genus, topological classification of minimal surfaces, uniqueness of Scherk singly periodic minimal surfaces, and outstanding problems and conjectures.
目次
Preface
Introduction
Basic results in classical minimal surface theory
Minimal surfaces with finite topology and more than one end
Limits of embedded minimal surfaces without local area or curvature bounds
The structure of minimal laminations of ℝ³
The Ordering Theorem for the space of ends
Conformal structure of minimal surfaces
Uniqueness of the helicoid I: proper case
Embedded minimal annular ends with infinite total curvature
The embedded Calabi–Yau problem
Local pictures, local removable singularities and dynamics
Embedded minimal surfaces of finite genus
Topological aspects of minimal surfaces
Partial results on the Liouville conjecture
The Scherk uniqueness theorem
Calabi–Yau problems
Outstanding problems and conjectures
Bibliography
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