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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles 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.

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Index bounds for free boundary minimal surfaces of convex bodies
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by Pam Sargent PDF
Proc. Amer. Math. Soc. 145 (2017), 2467-2480 Request permission

Abstract:

In this paper, we give a relationship between the eigenvalues of the Hodge Laplacian and the eigenvalues of the Jacobi operator for a free boundary minimal hypersurface of a Euclidean convex body. We then use this relationship to obtain new index bounds for such minimal hypersurfaces in terms of their topology. In particular, we show that the index of a free boundary minimal surface in a convex domain in $\mathbb {R}^3$ tends to infinity as its genus or the number of boundary components tends to infinity.
References
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Additional Information
  • Pam Sargent
  • Affiliation: Department of Mathematics, University of British Columbia, Vancouver, British Columbia, V6T 1Z2, Canada
  • Received by editor(s): May 31, 2016
  • Published electronically: February 10, 2017
  • Additional Notes: This work was partially supported by NSERC
  • Communicated by: Lei Ni
  • © Copyright 2017 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 145 (2017), 2467-2480
  • MSC (2010): Primary 49Q05; Secondary 47A75, 37B30
  • DOI: https://doi.org/10.1090/proc/13442
  • MathSciNet review: 3626504