Smoothness of Lipschitz-continuous graphs with nonvanishing Levi curvature

By Giovanna Citti, E. Lanconelli, A. Montanari. 2002

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In (1), (2), ~=(x , y, t) denotes the point of R 3, ut is the first derivative of u with respect to t, and analogous notations are used for the other firstand second-order derivatives of u. The notion of Levi curvature for a real manifold was introduced by E.E. Levi in 1909 in order to characterize the holomorphy domains of C 2. Since then, it has played a crucial role in the geometric theory of several complex variables. In looking for the polynomial hull of a graph, Slodkowski and Tomassini implicitly introduced in 1991 the following definition of Levi curvature for Lipschitz-continuous graphs [16].

Subfields: Applied Mathematics, Astronomy and Astrophysics

View Paper: https://www.semanticscholar.org/paper/4fd84fcb689172941d036c77b369956c727a3e81

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In Applied Mathematics

In Astronomy and Astrophysics

Citations in the corpus

Fundamental solutions for non-divergence form operators on stratified groups (2003, background): “These equations arise in many dierent settings: geometric theory of several complex variables, curvature problems for CR-manifolds, sub-Riemannian geometry, diusion processes, control theory, human vision; see, e.g., [ 15 , 16, 22, 23, 28, 29, 34, 36, 37, 40, 41, 43].”
IMPLICIT FUNCTION THEOREM IN CARNOT–CARATHÉODORY SPACES (2006, background): “This point of view was taken in the papers [4, 5, 8], where a surface with prescribed curvature was studied.”