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arXiv · 2609.03711

Chern's Conjecture with Constant Cubic Trace

Huixin Tan·Zizhou Tang·Yuquan Xie·Wenjiao Yan
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Abstract

We prove that the values set of \(S=|A|^2\) attained by closed embedded minimal hypersurfaces in \(\mathbb S^{n+1}(1)\) with constant \(S\) and constant \(f_3=\operatorname{tr}(A^3)\) is locally finite, where \(A\) denotes the shape operator. Neither the topology of the hypersurface nor the value of \(f_3\) is fixed.

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Huixin Tan, Zizhou Tang, Yuquan Xie, Wenjiao Yan. 2026-09-03. Chern's Conjecture with Constant Cubic Trace. https://arxiv.org/abs/2609.03711

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