Searcharxiv⌕ Search

arXiv subjects

Shengliang Pan

Publications and source records attributed to Shengliang Pan.

5 recordsLinked to original sources
arXiv2026

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

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.

math.DG↗
arXiv2026

A comparison theorem with applications to sharp geometric inequalities for submanifolds

In this paper, we derive an explicit expression for the Jacobian determinant of the normal exponential map on a submanifold, establishing a relationship with its ambient counterpart. This formula leads to a new comparison theorem which is closely related to the comparison theorem of Heintze-Karcher. As applications, we obtain a Fenchel-Borsuk-Chern-Lashof-type inequality and a Willmore-Chen-type inequality on closed submanifolds in complete noncompact manifolds with nonnegative curvature and Euclidean volume growth.

math.DG↗
arXiv2026

A fourth-order area-preserving curve flow in centro-equiaffine geometry

In this paper, inspired by the work of Guan and Li (2015), we introduce a fourth-order centro-equiaffine invariant curve flow via the affine Minkowski formula. Without any smallness assumptions on the initial curve, we establish the long-time existence of the flow and prove that, as $t \to +\infty$, the evolving curve preserves its enclosed area and converges smoothly to a round circle up to the action of $\mathrm{SL}(2)$.

math.DG↗