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math.AP2024
Some recent developments on isometric immersions via compensated compactness and gauge transforms
Siran Li
We survey recent developments on the analysis of Gauss--Codazzi--Ricci equations, the first-order PDE system arising from the classical problem of isometric immersions in different…
math.DG2024
On local solubility of Bao--Ratiu equations on surfaces related to the geometry of diffeomorphism group
Siran Li, Xiangxiang Su
We are concerned with the existence of asymptotic directions for the group of volume-preserving diffeomorphisms of a closed 2-dimensional surface within the full diffeomorp…
math.DG2024
On the fundamental theorem of submanifold theory and isometric immersions with supercritical low regularity
Siran Li, Xiangxiang Su
A fundamental result in global analysis and nonlinear elasticity asserts that given a solution to the Gauss--Codazzi--Ricci equations over a simply-connected closed…