Monochromatic Finsler surfaces and a local ellipsoid characterization

Monochromatic metrics are generalized Berwald

We show that monochromatic Finsler metrics, i.e., Finsler metrics such that each two tangent spaces are isomorphic as normed spaces, are generalized Berwald metrics, i.e., there exists an affine connection, possibly with torsion, that preserves the Finsler function

Banach等距猜想中的稳定性与近单色Finsler曲面

Stability in the Banach isometric conjecture and nearly monochromatic Finsler surfaces

本研究改进经典拓扑论证方法，得到Banach等距猜想k=2情形的稳定版本，同时证明非环面/克莱因瓶的近单色Finsler 2维曲面近似黎曼曲面，并用Banach-Mazur距离量化稳定性。

Average number of zeros and mixed symplectic volume of Finsler sets

Let $X$ be an $n$-dimensional manifold and $V_1, \ldots, V_n \subset C^\infty(X, \mathbb R)$ finite-dimensional vector spaces with Euclidean metric. We assign to each $V_i$ a Finsler ellipsoid, i.e., a family of ellipsoids in the fibers of the cotangent bundle of $X$. We prove that the average number of isolated common zeros of $f_1 \in V_1, \ldots, f_n \in V_n$ is equal to the mixed symplectic volume of these Finsler ellipsoids. If $X$ is a homogeneous space of a compact Lie group and all vector spaces $V_i$ and their Euclidean metrics are invariant, then the average numbers of zeros satisfy …

Black Holes, Ellipsoids, and Nonlinear Waves in Pseudo-Finsler Spaces and Einstein Gravity

We model pseudo-Finsler geometries, with pseudo-Euclidean signatures of metrics, for two classes of four dimensional nonholonomic manifolds: a) tangent bundles with two dimensional base manifolds and b) pseudo-Riemannian/ Einstein manifolds. Such spacetimes are enabled with nonholonomic distributions and associated nonlinear connection structures and theirs metrics are solutions of the field equations in general relativity or in generalized gravity theories with nonholonomic variables. We rewrite the Schwarzschild metric in Finsler variables and use it for generating new classes of locally ani…

二维射影 Finsler 度量中反射焦散线的尖点

On cusps of caustics by reflection in two dimensional projective Finsler metrics

本文研究射影 Finsler 度量下凸平面区域中的 Finsler 台球，证明经历固定反射次数的反射焦散线至少具有四个尖点，推广了欧氏台球的相关结果。

$\eta$-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。