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arXiv · 2607.26462

Evolution of hypersurfaces in $(n+1)$-dimensional light-cone

Xinjie Jiang·Shengliang Pan·Yun Yang
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Abstract

In this paper, we investigate the evolutionary processes of hypersurfaces within half of the $(n+1)$-dimensional light-cone. Depending on the evolutionary processes, our focus extends to exploring variational problems associated with a smooth function $f(S_1,\cdots,S_n)$, where each $S_r$ denotes the $r$-th elementary symmetric polynomial, defined as the sum of all possible products of $r$ distinct principal curvatures. We present several fundamental properties related to these variational problems. Furthermore, we examine a curvature-type flow defined locally within the light-cone, establishing its perpetual existence and smooth convergence to a circle whose length is preserved and equal to that of the initial curve.

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Xinjie Jiang, Shengliang Pan, Yun Yang. 2026-07-29. Evolution of hypersurfaces in $(n+1)$-dimensional light-cone. https://arxiv.org/abs/2607.26462

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