[CvGmt News] One-day workshop

[magnani at dm.unipi.it]

Please, find attached the program of the workshop.
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A One-Day Workshop on Symmetry, Subharmonicity and Nonsmooth Vector Fields
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http://cvgmt.sns.it/event/220/

Date: Wednesday, Feb 22, 2012

Place: Aula Magna, Department of Mathematics, Pisa University

15:30-16:20 Ermanno Lanconelli (Bologna University)

Title. Some problems of gravitational symmetry in both Riemannian and
sub-Riemannian contexts.

Abstract. Let P be a connected solid of mass m and suppose that the
gravitational field of P outside this set is equal to the field
generated by the mass m concentrated at the origin. It follows that P is a
ball concentrated at the origin. From this symmetry result, proved by
Ahranov, Shier and Zalcman in 1981, one establishes a harmonic
characterisation of Euclidean balls. The present talk
will be concerned with this problem in both Riemannian and sub-Riemannian
perspectives.

16:30-17:20 Andrea Bonglioli (Bologna University)

Title. Subharmonic Functions in sub-Riemannian Settings. Characterizations
of subharmonicity.

Abstract. In this talk we describe mean value characterizations for
subharmonic functions related to linear second order partial dierential
operators with non-negative characteristic form, possessing a well-behaved
fundamental solution Gamma. These characterizations are based on suitable
average operators on the level sets of Gamma. Asymptotic characterizations
are also considered. We
analyze as well the notion of subharmonic function in the weak sense of
distributions, and we show how to approximate subharmonic functions by
smooth ones. The classes of operators involved are wide enough to include,
as very
special cases, the sub-Laplacians on Carnot groups.

17:20-17:40 Coffee break

17:40-18:30 Daniele Morbidelli (Bologna University)

Title. Exponential maps and integrability results for nonsmooth
distributions.

Abstract. We will present some integrability results for distributions
spanned by families of nonsmooth vector fields. This involves the
discussion of the notion of commutator for vector fields with rough
coefficients. Our integrability results are also related with some
properties of a class of almost exponential maps which we discuss under
low regularity assumptions. These are joint results with Annamaria
Montanari (arXiv:1106.2410v2, arXiv:1201.5228, arXiv:1201.5209).

Organizing Commitee: V. Magnani

Invited Speakers: A. Bonfiglioli, E. Lanconelli, D. Morbidelli

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