“I can think, I can fast, I can wait.”

- Hermann Hesse -

[1]  (with Gui-Qiang G. Chen) Global Weak Rigidity of the Gauss--Codazzi--Ricci Equations and Isometric Immersions of Riemannian Manifolds with Lower Regularity,  J. Geom. Anal. 28 (2018), 1957–2007. [link]

Geometric Analysis and PDE

[6] On the Existence of $C^{1,1}$ Isometric Immersions of Several Classes of Negatively Curved Surfaces into $\mathbb{R}^3$. Arch. Ration. Mech. Anal. 236 (2020), 419–449. [pdf]

* Supplementary materials: Siran Li_isometric immerions of negatively curved surfaces. Mathematica code.nb [HERE]

[8]  (with Gui-Qiang G. Chen) Weak Continuity of the Cartan Structural System on Semi-Riemannian Manifolds with Lower Regularity. ArXiv: 1905.02661; submitted [pdf]. 

[14]  (with Robert Hardt) General Axially Symmetric Harmonic Maps. In preparation (2019).

[3]   A Remark on the Non-Compactness of $W^{2,d}$ Immersions of $d$-Dimensional Hypersurfaces. Arxiv: 1807.00360; accepted by Proc. Amer. Math. Soc (2019). [pdf]

[4]   Stability of Minimising Harmonic Maps under $W^{1,p}$ Perturbations of Boundary Data: $p \geq 2$. Arxiv: 1810.10599; submitted. [pdf]

[5] A Note on Generic Transversality of Euclidean Submanifolds, Manuscripta Math. 162 (2020), no. 1-2, 213–219 [pdf]

[13] (with Armin Schikorra) $W^{s,n/s}$-maps with positive distributional Jacobians; to appear in Potential Analysis, [link]

[7] Counterexamples to the $L^p$-Calderon--Zygmund Estimate on Open Manifolds. Ann. Global Anal. Geom. 57 (2020), 61–70. [pdf]

[9]  Towards a Theory of Multi-Parameter Geometrical Variational Problems: Fibre Bundles, Differential Forms and Riemannian Quasiconvexity. Arxiv: 1905.01410. To appear in Quart. Appl. Math. (2020) [pdf]

[10] A Note on Alberti's Luzin-Type Theorem for Gradients, Arxiv: 1910.02537. To appear in Ricerche di Math. (2020) [pdf]

[11] Optimal regularity for the Pfaff system and isometric immersions in arbitrary dimensions, submitted; ArXiv: 2003.05595 [pdf]

[15]  (with Galia Dafni) Necas Inequality, Inverse of Divergence and Compensated Compactness on Open Manifolds. In preparation (2019).