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Monotonicity Formulas For Diffusion Operators On Manifolds And Carnot Groups, Heat Kernel Asymptotics And Wiener's Criterion On Heisenberg-Type Groups, Kevin L. Rotz

Open Access Dissertations

The contents of this thesis are an assortment of results in analysis and subRiemannian geometry, with a special focus on the Heisenberg group Hn, Heisenbergtype (H-type) groups, and Carnot groups.

As we wish for this thesis to be relatively self-contained, the main definitions and background are covered in Chapter 1. This includes basic information about Carnot groups, Hn, H-type groups, diffusion operators, and the curvature dimension inequality.

Chapter 2 incorporates excerpts from a paper by N. Garofalo and the author, [42]. In it, we propose a generalization of Almgren’s frequency function N : (0, 1) → R for solutions to …