Estimating the Morse index of free boundary minimal hypersurfaces through covering arguments

Published 5 Jun 2022 in math.DG | (2206.02105v3)

Abstract: Given a compact Riemannian manifold, of dimension between 3 and 7, with boundary, we adapt Song's method in Song (2023) to the free boundary case to show that the Morse index of a free boundary minimal hypersurface grows linearly with the sum of its Betti numbers, where the constant of growth depends on the area of the free boundary minimal hypersurface in question.

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