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A conjecture of Antoni Zygmund
Antonio Córdoba, Eric Latorre, Ángel D. Martínez
In this paper we establish an exponential covering theorem implying a conjecture formulated by A. Zygmund circa 1935 whose three-dimensional case was obtained by the first named au…
Global well-posedness of critical surface quasigeostrophic equation on the sphere
Diego Alonso-Oran, Antonio Cordoba, Angel D. Martinez
In this paper we prove global well-posedness of the critical surface quasigeostrophic equation on the two dimensional sphere building on some earlier work of the authors. The proof…
Continuity of weak solutions of the critical quasigeostrophic equation on the sphere
Diego Alonso-Oran, Antonio Cordoba, Angel D. Martinez
In this paper we provide regularity results for active scalars that are weak solutions of almost critical drift-diffusion equations in general surfaces. This includes models of ani…
Integral representation for fractional Laplace-Beltrami operators
Diego Alonso-Oran, Antonio Cordoba, Angel D. Martinez
In this paper we provide an integral representation of the fractional Laplace-Beltrami operator for general riemannian manifolds which has several interesting applications. We give…