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