6 papers
Capillary Orlicz-Minkowski flow in the upper half-space
Guanghan Li, Chenyang Liu
In this paper, we study the long-time existence and asymptotic behavior of an anisotropic capillary Gauss curvature flow. By studying this flow and proving its convergence to a sta…
Alexandrov-Fenchel inequalities for convex anisotropic capillary hypersurfaces in the half-space
Jinyu Gao, Guanghan Li
In this paper, the results of Mei, Wang, Weng and Xia [Math. Z., 2025, MR4911815] on capillary convex bodies are extended to the anisotropic setting. We develop a theory for anisot…
Semantic Convergence: Harmonizing Recommender Systems via Two-Stage Alignment and Behavioral Semantic Tokenization
Guanghan Li, Xun Zhang, Yufei Zhang +3
Large language models (LLMs), endowed with exceptional reasoning capabilities, are adept at discerning profound user interests from historical behaviors, thereby presenting a promi…
Anisotropic mean curvature type flow and capillary Alexandrov-Fenchel inequalities
Shanwei Ding, Jinyu Gao, Guanghan Li
In this paper, an anisotropic volume-preserving mean curvature type flow for star-shaped anisotropic -capillary hypersurfaces in the half-space is studied, and the long-time e…
Locally constrained flows and geometric inequalities in sphere
Shanwei Ding, Guanghan Li
In this paper, we uncover an intriguing algebra property of an element symmetric polynomial. By this property, we establish the longtime existence and convergence of a locally cons…
Generalized Minkowski formulas and rigidity results for anisotropic capillary hypersurfaces
Jinyu Gao, Guanghan Li
In this paper, we obtain a new Hsiung-Minkowski integral formula for anisotropic capillary hypersurfaces in the half-space, which includes the weighted Hsiung-Minkowski formula and…