PUBLICATIONS
Geometric Analysis and PDE
[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]
[2] (with Gui-Qiang G. Chen) Compensated Compactness in Banach Spaces and Weak Rigidity of Isometric Immersions of Manifolds. To appear in Helge Holden's 60th birthday volume, Non-linear partial differential equations, mathematical physics, and stochastic analysis, 73–95, EMS Ser. Congr. Rep., Eur. Math. Soc., Zürich, 2018. (*Exposition for [1])
[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]
[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]
[7] Counterexamples to the $L^p$-Calderon--Zygmund Estimate on Open Manifolds. Ann. Global Anal. Geom. 57 (2020), 61–70. [pdf]
[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].
[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]
[12] The Weyl problem of isometric immersions revisited, To appear in Bulletin London Math. Soc.; ArXiv: 2004.05532 [pdf]
[13] (with Armin Schikorra) $W^{s,n/s}$-maps with positive distributional Jacobians; to appear in Potential Analysis, [link]
[14] (with Robert Hardt) General Axially Symmetric Harmonic Maps. In preparation (2019).
[15] (with Galia Dafni) Necas Inequality, Inverse of Divergence and Compensated Compactness on Open Manifolds. In preparation (2019).
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[2] (with Gui-Qiang G. Chen) Compensated Compactness in Banach Spaces and Weak Rigidity of Isometric Immersions of Manifolds. To appear in Helge Holden's 60th birthday volume, Non-linear partial differential equations, mathematical physics, and stochastic analysis, 73–95, EMS Ser. Congr. Rep., Eur. Math. Soc., Zürich, 2018. (*Exposition for [1])
[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]
[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]
[7] Counterexamples to the $L^p$-Calderon--Zygmund Estimate on Open Manifolds. Ann. Global Anal. Geom. 57 (2020), 61–70. [pdf]
[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].
[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]
[12] The Weyl problem of isometric immersions revisited, To appear in Bulletin London Math. Soc.; ArXiv: 2004.05532 [pdf]
[13] (with Armin Schikorra) $W^{s,n/s}$-maps with positive distributional Jacobians; to appear in Potential Analysis, [link]
[14] (with Robert Hardt) General Axially Symmetric Harmonic Maps. In preparation (2019).
[15] (with Galia Dafni) Necas Inequality, Inverse of Divergence and Compensated Compactness on Open Manifolds. In preparation (2019).