Submanifolds in carnot groups

著者

• Vittone, Davide

書誌事項

Submanifolds in carnot groups

Davide Vittone

（Tesi = theses, 7）

Edizioni della Normale, Scuola Normale Superiore, c2008

注記

Includes bibliographical references

内容説明・目次

内容説明

The book is devoted to the study of submanifolds in the setting of Carnot groups equipped with a sub-Riemannian structure; particular emphasis is given to the case of Heisenberg groups. A Geometric Measure Theory viewpoint is adopted, and features as intrinsic perimeters, Hausdorff measures, area formulae, calibrations and minimal surfaces are considered. Area formulae for the measure of submanifolds of arbitrary codimension are obtained in Carnot groups. Intrinsically regular hypersurfaces in the Heisenberg group are extensively studied: suitable notions of graphs are introduced, together with area formulae leading to the analysis of Plateau and Bernstein type problems.

目次

Preface.- 1. Carnot groups.- 2. Measure of submanifolds on Carnot groups.- 3. Elements of Geometric Measure Theory in the Heisenberg group.- 4. Intrinsic parametrization of H-regular surfaces.- 5. The Bernstein problem in Heisenberg groups and calibrations.

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詳細情報

• NII書誌ID(NCID): BA86115360
• ISBN:
  • 9788876423277
• 出版国コード: it
• タイトル言語コード: eng
• 本文言語コード: eng
• 出版地: Pisa
• ページ数/冊数: xx, 180 p.
• 大きさ: 24 cm
• 件名:
  • LCSH : Submanifolds
  • LCSH : Geometric measure theory
  • LCSH : Geometry, Differential
• 親書誌ID:
  • BA86073952