4 papers
Generalized Hamiltonian gradient flow of contact type I: regularity of the fundamental solutions
Wei Cheng, Shengqing Hu, Kaizhi Wang
This paper studies generalized Hamiltonian gradient flows for contact-type Hamilton--Jacobi equations, adopting the variational framework of Herglotz's principle and its fundamenta…
A proof of Toponogov's theorem in Alexandrov geometry
Shengqi Hu, Xiaole Su, Yusheng Wang
This paper aims to give an elementary proof for Toponogov's theorem in Alexandrov geometry with lower curvature bound. The idea of the proof comes from the fact that, in Riemannian…
New definitions of Alexandrov space and applications
Shengqi Hu, Xiaole Su, Yusheng Wang
In this paper we show that, in the definition of Alexandrov spaces with lower or upper curvature bound, the original conditions can be replaced with much weaker ones. For the purpo…
Representation formulas for contact type Hamilton-Jacobi equations
Jiahui Hong, Wei Cheng, Shengqing Hu +1
We discuss various kinds of representation formulas for the viscosity solutions of the contact type Hamilton-Jacobi equations by using the Herglotz' variational principle.