Author

Siran Li

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Preprint Sep 2026

A geometric rigidity estimate for codimension-1 immersions into spheres

We establish a quantitative stability estimate for codimension-one immersions into a round sphere. Let $(M,g)$ be an oriented Riemannian manifold and suppose that a prescribed shape operator is realised by a smooth isometric immersion $\theta:(M,g)\to\mathbb S^{n+1}$. We prove that, on every relatively compact strongly...

Si-Ran Li, I. Newell · 0 citations

Preprint Sep 2026

The hedgehog uniquely minimises every $p$-energy

We prove that for every dimension $n \geq 2$ and parameter $p \in ]1,n[$, the hedgehog $u_0(x) = x/|x|$ is the unique minimiser of the $p$-energy $\mathcal{E}_p [u]:=\int_{\mathbf{B}^n}|\nabla u|^p\,{\rm d}x$ in the class of $W^{1,p}$-mappings from the $n$-dimensional unit ball $\mathbf{B}^n$ to the $(n-1)$-dimensional...

Si-Ran Li · 0 citations

Preprint Jul 2026

On well-posedness theory of very weak solutions to Navier-Stokes equations on irregular domains with nonhomogeneous Dirichlet boundary data

The well-posedness theory of very weak solutions is a central topic in mathematical hydrodynamics, especially in the regularity theory for Navier-Stokes equations. It has been fully developed for incompressible fluid flows on bounded domains in R^3 of C^{2,1}-regularity. In this paper, based on the analytic theories in...

Xiaojin Bai, Siran Li, Xiangxiang Su · 0 citations