Geometry of hypersurfaces in Carnot groups of step 2
Abstract
This thesis consists of a variety of results pertaining to the analysis of hyper-surfaces in Carnot groups of step 2. Chapter 3 provides an extension of a function u ∈ BVH(Ω) to a function u0 ∈ BVH([special characters omitted]), when Ω ⊂ [special characters omitted] is H-admissible, and [special characters omitted] is a step 2 Carnot group. It is shown that H-admissible domains include non-characteristic domains and domains in groups of Heisenberg type which have a partial symmetry about characteristic points. An example is given of a domain Ω that is C1,α, α < 1, that is not H-admissible. Further, when Ω is H-admissible a trace theorem is proved for u ∈ BVH(Ω). Chapter 4 studies hypersurfaces that are Xi graphs. A first and second variation formula are proved, and the notion of flow by horizontal mean curvature is analyzed for Xi-graphs. A first and second variation formula is also proved in chapter 5 using an ε-approximation technique. This technique also is used to prove several integration by parts formulas.
Degree
Ph.D.
Advisors
Garofalo, Purdue University.
Subject Area
Mathematics
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