Siran Li

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20232026

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math.DG2026

Existence of semiglobal $W^{2, p}$ -isometric immersions for negatively curved surface metrics with unbounded second fundamental form

Siran Li

This paper is concerned with the existence theory of isometric immersions of surfaces with negative Gaussian curvature into the three-dimensional Euclidean space. We reformulate th…

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 $(Σ, g)$ 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 $S$ to the Gauss--Codazzi--Ricci equations over a simply-connected closed…

math.DG2023

A smooth isotopy of volume-preserving diffeomorphisms on unit cube saving energy through extra dimensions

Siran Li

We construct an explicit example of a smooth isotopy ${ξ_{t}}_{t \in [0, 1]}$ of volume- and orientation-preserving diffeomorphisms on $[0, 1]^{n}$ ( $n \geq 3$ ) that has infinite total…

Existence of semiglobal W2,p-isometric immersions for negatively curved surface metrics with unbounded second fundamental form

On local solubility of Bao--Ratiu equations on surfaces related to the geometry of diffeomorphism group

On the fundamental theorem of submanifold theory and isometric immersions with supercritical low regularity

A smooth isotopy of volume-preserving diffeomorphisms on unit cube saving energy through extra dimensions

Existence of semiglobal $W^{2, p}$ -isometric immersions for negatively curved surface metrics with unbounded second fundamental form