4 papers
Some aspects of Cheng-Yau gradient estimates
Qixuan Hu, Chengjie Yu
In this note, we extend the rigidity of Cheng-Yau gradient estimate in \cite{HXY} to surfaces with lower Ricci curvature bound. Motivated by these sharp Cheng-Yau gradient estimate…
Fundamental Theorem for Submanifolds in General Ambient Spaces
Chengjie Yu
In this paper, we extend the fundamental theorem for submanifolds to general ambient spaces by viewing it as a higher codimensional Cartan-Ambrose-Hicks theorem. The key ingredient…
Extensions of isometric immersions and Cartan-Ambrose-Hicks theorem based on submanifolds
Chengjie Yu
In this paper, we study the general extension problem for isometric immersions by establishing Cartan-Ambrose-Hicks theorems based on submanifolds. Our method also provides geometr…
Developments of curves with respect to symmetric tensors and existence of isometric immersions with prescribed second fundamental form
Chengjie Yu
In this paper, we introduce the notion of developments of curves with respect to symmetric tensors and use it to prove the existence of isometric immersions into a general ambient…