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Advances in Calculus of Variations

Managing Editor: Duzaar, Frank / Kinnunen, Juha

Editorial Board: Armstrong, Scott N. / Balogh, Zoltán / Cardiliaguet, Pierre / Dacorogna, Bernard / Dal Maso, Gianni / DiBenedetto, Emmanuele / Fonseca, Irene / Gianazza, Ugo / Ishii, Hitoshi / Kristensen, Jan / Manfredi, Juan / Martell, Jose Maria / Mingione, Giuseppe / Nystrom, Kaj / Riviére, Tristan / Schaetzle, Reiner / Shen, Zhongwei / Silvestre, Luis / Tonegawa, Yoshihiro / Touzi, Nizar / Wang, Guofang


IMPACT FACTOR 2017: 1.676

CiteScore 2017: 1.30

SCImago Journal Rank (SJR) 2017: 2.045
Source Normalized Impact per Paper (SNIP) 2017: 1.138

Mathematical Citation Quotient (MCQ) 2017: 1.15

Online
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1864-8266
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Volume 1, Issue 3

Issues

Comparison between second variation of area and second variation of energy of a minimal surface

Norio Ejiri
  • Department of Mathematics, Faculty of Science and Technology, Meijo University, 1-501 Shiogamaguchi, Tempaku-ku, Nagoya-shi, Aichi 468-8502, Japan. E-mail:
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/ Mario Micallef
Published Online: 2008-11-25 | DOI: https://doi.org/10.1515/ACV.2008.009

Abstract

We show that the difference between the Morse index of a closed minimal surface as a critical point of the area functional and its Morse index as a critical point of the energy is at most the real dimension of Teichmüller space. This enables us to bound the index of a closed minimal surface in an arbitrary Riemannian manifold by the area and genus of the surface, and the dimension and geometry of the ambient manifold. Our method also yields surprisingly good upper bounds on the index of a minimal surface of finite total curvature in Euclidean space of any dimension.

Keywords.: Minimal surface; harmonic map; Morse index

About the article

Received: 2007-08-16

Revised: 2007-08-30

Published Online: 2008-11-25

Published in Print: 2008-10-01


Citation Information: Advances in Calculus of Variations, Volume 1, Issue 3, Pages 223–239, ISSN (Online) 1864-8266, ISSN (Print) 1864-8258, DOI: https://doi.org/10.1515/ACV.2008.009.

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Inventiones mathematicae, 2017, Volume 209, Number 3, Page 617
[2]
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Inventiones mathematicae, 2016, Volume 203, Number 3, Page 823

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