Some recent developments on isometric immersions via compensated compactness and gauge transforms
S Li - arXiv preprint arXiv:2409.08922, 2024 - arxiv.org
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 differential …
order PDE system arising from the classical problem of isometric immersions in differential …
The isometric immersion of surfaces with finite total curvature
In this paper, we study the smooth isometric immersion of a complete simply connected
surface with a negative Gauss curvature in the three-dimensional Euclidean space. For a …
surface with a negative Gauss curvature in the three-dimensional Euclidean space. For a …
Wedge product theorem in compensated compactness theory with critical exponents on Riemannian manifolds
S Li - arXiv preprint arXiv:2307.13175, 2023 - arxiv.org
We formulate and prove compensated compactness theorems concerning the limiting
behaviour of wedge products of weakly convergent differential forms on closed Riemannian …
behaviour of wedge products of weakly convergent differential forms on closed Riemannian …
Weak continuity of curvature for connections in
GQG Chen, TP Giron - arXiv preprint arXiv:2108.13529, 2021 - arxiv.org
We study the weak continuity of two interrelated non-linear partial differential equations, the
Yang-Mills equations and the Gau {\ss}-Codazzi-Ricci equations, involving $ L^ p …
Yang-Mills equations and the Gau {\ss}-Codazzi-Ricci equations, involving $ L^ p …
On the Existence of -isometric Immersions of Several Classes of Negatively Curved Surfaces into
S Li - Archive for Rational Mechanics and Analysis, 2020 - Springer
We prove the existence of C^ 1, 1 C 1, 1-isometric immersions of several classes of
negatively curved Riemannian surfaces (M, g)(M, g) into the 3-dimensional Euclidean space …
negatively curved Riemannian surfaces (M, g)(M, g) into the 3-dimensional Euclidean space …
On the Existence of Isometric Immersions of Several Classes of Negatively Curved Surfaces Into
S Li - arXiv preprint arXiv:1801.06767, 2018 - arxiv.org
We prove the existence of $ C^{1, 1} $ isometric immersions of several classes of metrics on
surfaces $(\mathcal {M}, g) $ into the three-dimensional Euclidean space $\mathbb {R}^ 3 …
surfaces $(\mathcal {M}, g) $ into the three-dimensional Euclidean space $\mathbb {R}^ 3 …