Finsler geometries on strictly accretive matrices

Regularity of Lipschitz boundaries with prescribed sub-Finsler mean curvature in the Heisenberg group $\mathbb{H}^1$

For a strictly convex set $K\subset \mathbb{R}^2$ of class $C^2$ we consider its associated sub-Finsler $K$-perimeter $|\partial E|_K$ in $\mathbb{H}^1$ and the prescribed mean curvature functional $|\partial E|_K-\int_E f$ associated to a function $f$. Given a critical set for this functional with Euclidean Lipschitz and intrinsic regular boundary, we prove that their characteristic curves are of class $C^2$ and that this regularity is optimal. The result holds in particular when the boundary of $E$ is of class $C^1$.

次芬斯勒ℓ^p-海森堡群的测度收缩性质、曲率指数与测地线维数

Measure contraction property, curvature exponent and geodesic dimension of sub-Finsler $\ell^p$-Heisenberg groups

该研究首次探索次芬斯勒几何的合成曲率-维数界，分析ℓ^p-海森堡群的测度收缩性质与测地线维数，明确不同p取值下的性质成立条件，并给出首个曲率指数与测地线维数存在间隙的度量测度空间实例。

$\eta$-一致凸性与可除域

$β$-Uniform Convexity and Divisible Domains

本文证明严格凸可除域上的自然芬斯勒度量具有$\eta$-一致凸性，常数$\eta$与边界正则性相关，并借助AI辅助证明希尔伯特度量在适当假设下也满足该性质。

次芬斯勒流形中曲率-维数条件的失效

Failure of the curvature-dimension condition in sub-Finsler manifolds

本文将次黎曼几何中曲率-维数条件不成立的结果推广到次芬斯勒流形，证明CD(K,N)在光滑强凸范数及C^{1,1}范数情形下均失效，并进一步证明海森堡群中更弱的MCP(K,N)也不成立，为此引入新工具与思想。

Infinite geodesics and isometric embeddings in Carnot groups of step 2

In the setting of step 2 sub-Finsler Carnot groups with strictly convex norms, we prove that all infinite geodesics are lines. It follows that for any other homogeneous distance, all geodesics are lines exactly when the induced norm on the horizontal space is strictly convex. As a further consequence, we show that all isometric embeddings between such homogeneous groups are affine. The core of the proof is an asymptotic study of the extremals given by the Pontryagin Maximum Principle.