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Index bounds for free boundary minimal surfaces of convex bodies


Author: Pam Sargent
Journal: Proc. Amer. Math. Soc. 145 (2017), 2467-2480
MSC (2010): Primary 49Q05; Secondary 47A75, 37B30
DOI: https://doi.org/10.1090/proc/13442
Published electronically: February 10, 2017
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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.


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Additional Information

Pam Sargent
Affiliation: Department of Mathematics, University of British Columbia, Vancouver, British Columbia, V6T 1Z2, Canada

DOI: https://doi.org/10.1090/proc/13442
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
Article copyright: © Copyright 2017 American Mathematical Society