Siran Li   李思然

(Courtesy due to Dr. Betul Orcan-Ekmekci and Dr. Yixing Wu)

I am a postdoc in mathematics based at Rice University, USA. My research interests lie in analysis, PDE (Partial Differential Equation), calculus of variations, and applied maths. My CV can be found here (updated on 12 Dec 2019).

From 2009--2013 I read maths (BA) at Columbia University, NY. I obtained my D.Phil. from the University of Oxford, UK in 2017 under the supervision of Prof. Gui-Qiang G. Chen. My mentor

at Rice University is Prof. Robert M. Hardt

Research Interests

  • Calculus of variations and GMT (geometric measure theory).

  • Geometric analysis and global analysis.

  • PDE arising in geometry and physics.

  • Applied mathematics; in particular, continuum mechanics and statistics.

Recent Activities

  • The following preprint is now available on ArXiv: Optimal regularity for the Pfaff system and isometric immersions in arbitrary dimensions, 2003.05595. [pdf]

       In this paper, we proved the existence of weak W^{1,2}-solutions for the Pfaff system with $L^2$-antisymmetric coefficient matrix. Thus, we established the equivalence between the existence of $W^{2,2}$-isometric immersions on simply-connected domains and the solubility of Gauss--Codazzi--Ricci equations in $L^2$. 

       This result is sharp: one cannot further relax the regularity assumptions. Our result is the optimal regularity version of the classical work by Hartman--Wintner in 1950, Amer. J. Math. The proof relies on Uhlenbeck's theorem on Coulomb gauges.

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