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Mathematics & Statistics

Differential Geometry
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Friday, September 20, 2019

Title
Speaker
Time
Place

On Level Sets in the Heisenberg Group
Zachary Forest
11:00am-12:00pm
NES 104

Abstract

It is known that in Euclidean geometry the \(p\)-Laplace Equation supports a level-set removability property for weak solutions; however, such results are still largely unknown in the class of sub-Riemannian manifolds. Even in spaces such as the Heisenberg group, the simplest nontrivial sub-Riemannian manifold, the question of removability has remained open for years. In this talk we ask the question, "can level-set removability be extended for the Heisenberg group \(\mathbb{H}_1\)?", and thanks to papers by Juutinen and Lindqvist (2005) and Franci-Serapioni-Serra Cassano (2001) can answer it in the affirmative for viscosity solutions to the horizontal \(p\)-Laplacian and horizontal \(p(x)\)-Laplacian under certain regularity conditions.

Friday, September 13, 2019

Title
Speaker
Time
Place

Rado-type Removability Results for \(p\)-Laplace and \(p(x)\)-Laplace in the Heisenberg group
Bob Freeman
11:00am-12:00pm
NES 104

Abstract

We recall the Rado-type removability results for \(p\)-harmonic functions in the plane (Kilpelainen 1994) and the extension to quasi-linear functions in Euclidean space (Juutinen, Lindqvist 2005). We discuss new removability results for solutions to the \(p\)-Laplace and the \(p(x)\)-Laplace equations in the Heisenberg group.