The stability index and Yau's conjecture for Carlotto-Schulz minimal hypertori

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Bibliographic Details
Main Author:	Perdomo, Oscar
Format:	Preprint
Published:	2025
Subjects:	Differential Geometry 53C42, 58J50
Online Access:	Acceder al recurso
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_version_	1866916948576567296
author	Perdomo, Oscar
author_facet	Perdomo, Oscar
contents	Recently, for any n>1, Carlotto and Schulz showed the existence of a minimal embedding in the 2n-dimensional unit sphere. In this paper, we show that the stability index of these embedded minimal hypersurfaces is at least n^2+4n+3. We also show that Yau's conjecture holds for these examples if and only if the solution of the differential equation z''(t)+a_n(t)z'(t)+(2n-1)z(t)=0 with z(0)=1 and z'(0)=0 satisfies z'(T)>0. Here,T and the T-periodic function a_n(t) are determined in terms of the functions defining the minimal immersion.
format	Preprint
id	arxiv_https___arxiv_org_abs_2508_09104
institution	arXiv
publishDate	2025
record_format	arxiv
spellingShingle	The stability index and Yau's conjecture for Carlotto-Schulz minimal hypertori Perdomo, Oscar Differential Geometry 53C42, 58J50 Recently, for any n>1, Carlotto and Schulz showed the existence of a minimal embedding in the 2n-dimensional unit sphere. In this paper, we show that the stability index of these embedded minimal hypersurfaces is at least n^2+4n+3. We also show that Yau's conjecture holds for these examples if and only if the solution of the differential equation z''(t)+a_n(t)z'(t)+(2n-1)z(t)=0 with z(0)=1 and z'(0)=0 satisfies z'(T)>0. Here,T and the T-periodic function a_n(t) are determined in terms of the functions defining the minimal immersion.
title	The stability index and Yau's conjecture for Carlotto-Schulz minimal hypertori
topic	Differential Geometry 53C42, 58J50
url	https://arxiv.org/abs/2508.09104

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