arXiv subjects

Lishan Li

Publications and source records attributed to Lishan Li.

3 recordsLinked to original sources

arXiv2026

Generalized Hyperbolic Conical Circle Packings associated with Finite Polygonal Decompositions of Surfaces with Boundary

Let S be a compact topological surface with finitely many genus and finitely many holes and let D be a polygonal decomposition of S. In this paper, we consider the generalized hyperbolic conical circle packings associated with D. We first show that the boundary value problem has a unique solution k by prescribing total geodesic curvatures of generalized hyperbolic conical circles centered at interior vertices and geodesic curvatures of generalized hyperbolic conical circles centered at boundary vertices. Then we show that such a solution k can be obtained by taking a limit of the packings inductively modified by Thurston's algorithm via an arbitrarily chosen initial generalized hyperbolic conical circle packing associated with D and with given boundary values. Thirdly, we develop the so-called discrete Schwarz-Pick lemma for the solution packing k on D.

math.GT↗

arXiv2026

Perron's method and spherical ideal circle patterns with prescribed total geodesic curvatures

In this paper, we apply the classical Perron method to give a proof of the existence and uniqueness/rigidity result of a circle pattern on a closed surface equipped with conical spherical metric when prescribed measures of the angles of intersecting circles stay in the range (0,{\pi}/2] and total geodesic curvatures are assigned to the circles, which is recently obtained in [3] via Colin de Verdi\`ere's variation method. Then we show the convergence of Thurston's algorithm, which adjusts the geodesic curvatures of circles one by one based on the prescribed values for total geodesic curvatures of the circles, to the desired circle pattern in the setting of the result.

math.GT↗

arXiv2025

Multi-modal Transfer Learning for Dynamic Facial Emotion Recognition in the Wild

Facial expression recognition (FER) is a subset of computer vision with important applications for human-computer-interaction, healthcare, and customer service. FER represents a challenging problem-space because accurate classification requires a model to differentiate between subtle changes in facial features. In this paper, we examine the use of multi-modal transfer learning to improve performance on a challenging video-based FER dataset, Dynamic Facial Expression in-the-Wild (DFEW). Using a combination of pretrained ResNets, OpenPose, and OmniVec networks, we explore the impact of cross-temporal, multi-modal features on classification accuracy. Ultimately, we find that these finely-tuned multi-modal feature generators modestly improve accuracy of our transformer-based classification model.

cs.CV↗