arXiv subjects

Annamaria Montanari

Publications and source records attributed to Annamaria Montanari.

21 records · Page 2Linked to original sources

arXiv2007

Integral formulas for a class of curvature PDE's and applications to isoperimetric inequalities and to symmetry problems

We prove integral formulas for closed hypersurfaces in C^{n+1}, which furnish a relation between elementary symmetric functions in the eigenvalues of the complex Hessian matrix of the defining function and the Levi curvatures of the hypersurface. Then we follow the Reilly approach to prove an isoperimetric inequality. As an application, we obtain the ``Soap Bubble Theorem'' for star-shaped domains with positive and constant Levi curvatures bounding the classical mean curvature from above.

math.AP↗

arXiv2003

On the second order derivatives of convex functions on the Heisenberg group

In the Euclidean setting the celebrated Aleksandrov-Busemann-Feller theorem states that convex functions are a.e. twice differentiable. In this paper we prove that a similar result holds in the Heisenberg group, by showing that every continuous H-convex function belongs to the class of functions whose second order horizontal distributional derivatives are Radon measures. Together with a recent result by Ambrosio and Magnani, this proves the existence a.e. of second order horizontal derivatives for the class of continuous H-convex functions in the Heisenberg group.

math.AP↗

arXiv2003

Maximum and comparison principles for convex functions on the Heisenberg group

We prove estimates, similar in form to the classical Aleksandrov estimates, for a Monge-Ampere type operator on the Heisenberg group. A notion of normal mapping does not seem to be available in this context and the method of proof uses integration by parts and oscillation estimates that lead to the construction of an analogue of Monge-Ampere measures for convex functions in the Heisenberg group.

math.AP↗