Skip to Main Content

Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

A note on the index of closed minimal hypersurfaces of flat tori
HTML articles powered by AMS MathViewer

by Lucas Ambrozio, Alessandro Carlotto and Ben Sharp PDF
Proc. Amer. Math. Soc. 146 (2018), 335-344 Request permission

Abstract:

Generalizing earlier work by Ros in ambient dimension three, we prove an affine lower bound for the Morse index of closed minimal hypersurfaces inside a flat torus in terms of their first Betti number (with purely dimensional coefficients).
References
  • L. Ambrozio, A. Carlotto, and B. Sharp, Comparing the Morse index and the first Betti number of minimal hypersurfaces, J. Differential Geom. (to appear).
  • M. do Carmo and M. Dajczer, Rotation hypersurfaces in spaces of constant curvature, Trans. Amer. Math. Soc. 277 (1983), no. 2, 685–709. MR 694383, DOI 10.1090/S0002-9947-1983-0694383-X
  • J. Choe and A. Fraser, Mean curvature in manifolds with Ricci curvature bounded from below, preprint (arXiv: 1605.06602).
  • J. Choe and J. Hoppe, Higher dimensional Schwarz’s surfaces and Scherk’s surfaces, preprint (arXiv: 1607.07153).
  • D. A. Hoffman, Some basic facts, old and new, about triply periodic embedded minimal surfaces, J. Physique 51 (1990), no. 23, Suppl. Colloq. C7, 197–208 (English, with French summary). International Workshop on Geometry and Interfaces (Aussois, 1990). MR 1090149
  • Edmund F. Kelly, Cohomology of compact minimal submanifolds, Michigan Math. J. 19 (1972), 133–135. MR 317241
  • C. Li, Index and topology of minimal hypersurfaces in $\mathbb {R}^n$, preprint (arXiv:1605.09693).
  • F. Marques, Minimal surfaces - variational theory and applications, Proceedings of the International Congress of Mathematicians, Seoul 2014.
  • William H. Meeks III, The theory of triply periodic minimal surfaces, Indiana Univ. Math. J. 39 (1990), no. 3, 877–936. MR 1078743, DOI 10.1512/iumj.1990.39.39043
  • Tadashi Nagano and Brian Smyth, Minimal varieties and harmonic maps in tori, Comment. Math. Helv. 50 (1975), 249–265. MR 390974, DOI 10.1007/BF02565749
  • A. Neves, New applications of Min-max Theory, Proceedings of the International Congress of Mathematicians, Seoul 2014.
  • Antonio Ros, One-sided complete stable minimal surfaces, J. Differential Geom. 74 (2006), no. 1, 69–92. MR 2260928
  • Marty Ross, Schwarz’ $P$ and $D$ surfaces are stable, Differential Geom. Appl. 2 (1992), no. 2, 179–195. MR 1245555, DOI 10.1016/0926-2245(92)90032-I
Similar Articles
  • Retrieve articles in Proceedings of the American Mathematical Society with MSC (2010): 53A10, 53C42, 49Q05
  • Retrieve articles in all journals with MSC (2010): 53A10, 53C42, 49Q05
Additional Information
  • Lucas Ambrozio
  • Affiliation: Department of Mathematics, Imperial College, South Kensington Campus, London SW7 2AZ, United Kingdom
  • Email: l.ambrozio@imperial.ac.uk
  • Alessandro Carlotto
  • Affiliation: ETH - Department of Mathematics, Rämistrasse 101, 8092 Zürich,Switzerland
  • MR Author ID: 925162
  • Email: alessandro.carlotto@math.ethz.ch
  • Ben Sharp
  • Affiliation: Department of Mathematics, University of Warwick, Gibbet Hill Road, Coventry CV4 7AL, United Kingdom
  • MR Author ID: 1008414
  • Email: b.sharp@warwick.ac.uk
  • Received by editor(s): January 24, 2017
  • Published electronically: August 1, 2017
  • Communicated by: Lei Ni
  • © Copyright 2017 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 146 (2018), 335-344
  • MSC (2010): Primary 53A10; Secondary 53C42, 49Q05
  • DOI: https://doi.org/10.1090/proc/13833
  • MathSciNet review: 3723144