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2023.
Fine structure of the singular set of area minimizing hypersurfaces modulo $p$.
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2022. 
The regularity theory for the area functional (in geometric measure theory). International Congress of Mathematicians.
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2022. 
An Allard-type boundary regularity theorem for $2d$ minimizing currents at smooth curves with arbitrary multiplicity.
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2021. 
Area minimizing hypersurfaces modulo $p$: a geometric free-boundary problem.
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2021. 
Instability and nonuniqueness for the 2d Euler equations in vorticity form, after M. Vishik.
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2021. 
Positive solutions of transport equations and classical nonuniqueness of characteristic curves. Arch. Ration. Mech. Anal. . 240(2):1055-1090.
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Almgren's center manifold in a simple setting. Harmonic Analysis and Applications. IAS/Park City Mathematics Series. 27
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2020. 
$C^{1,\alpha}$ isometric embeddings of polar caps. Adv. Math. 363
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2020. 
The generalized Caffarelli-Kohn-Nirenberg Theorem for the hyperdissipative Navier-Stokes system. Comm. Pure Appl. Math.. 73(3):609-663.
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2020. 
The Nash-Kuiper Theorem and the Onsager conjecture. ICCM Not.. 8(1):17-26.
Bejing-5.pdf (353.58 KB)
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2020. 
Regularity of area minimizing currents mod $p$. Geom. Funct. Anal.. 30((5)):1224-1336.
DLHMS_nonlinear_2.pdf (978.39 KB)
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2020. 
Regularity theory for 2-dimensional almost minimal currents III: blowup. J. Differential Geom.. 116(1):125-185.
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2020. 
A direct approach to the anisotropic Plateau problem. Adv. Calc. Var.. 12(2):211-223.
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2019. 
Lossless analog compression. IEEE Trans. Inform. Theory. 65(11):7480-7513.
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2019. 
The masterpieces of John Forbes Nash Jr.. The Abel Prize 2013-2017.
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2019. 
Min-max embedded geodesic lines on asymptotically conical surfaces. J. Differential Geom.. 112(3):411-445.
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2019. 
Onsager's conjecture for admissible weak solutions. Communications on Pure and Applied Mathematics. 72:229–274.
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Errata-Onsager.pdf (90.35 KB)
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2019. 

On turbulence and geometry: from Nash to Onsager. Notices Amer. Math. Soc.. 66(5)
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2019. 
Allard's interior regularity theorem: an invitation to stationary varifolds. Nonlinear analysis in geometry and applied mathematics.. 2:23-49.
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2018. 
Boundary regularity of mass-minimizing integral currents and a question of Almgren. Matrix Annals 2017. :193-205.
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2018. 
Ill-posedness of Leray solutions for the ipodissipative Navier–Stokes equations. Communications in Mathematical Physics. 362(2):659–688.
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2018. 
Min-max theory for minimal hypersurfaces with boundary. Annales de l'Institut Fourier. 68(5):1909–1986.
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2018. 