Index bounds for free boundary minimal surfaces of convex bodies
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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.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