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Showing 1 to 8 of 8 for “"Carnot Group"”.
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Analysis in the Heisenberg group: weak s-John domains and the dimensions of graphs of Holder functions
… R^n and analytic properties in sub-Riemannian Carnot groups. We introduce weak s-John domains, in analogy with weak John domains, and we prove that weak s-John is equivalent to a localized version. This is applied in showing that a bounded C^{1,alpha} domain in R^3 will be a weak s-John domain …
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Intrinsic Differentiability and Intrinsic Regular Surfaces in Carnot groups
… by Franchi, Serapioni, Serra Cassano in a Carnot group G. More precisely, an intrinsic regular hypersurface (i.e. a topological codimension 1 surface) S is a subset of G which is locally defined as a non critical level set of a C^1 intrinsic function. In a similar way, a k-codimensional …
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Lipschitz and Holder mappings into jet space Carnot groups
… functions in $C^k(\R^n)$. Warhurst constructs a Carnot group structure on $J^k(\R^n)$ such that the jets of functions in $C^{k+1}(\R^n)$ are horizontal. Like in all Carnot groups, one can define a Carnot-Carath\'eodory metric on $J^k(\R^n)$ by minimizing lengths of horizontal paths. …
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Functional inequalities and the curvature dimension inequality on totally geodesic foliations
… Ricci tensor bounds, K-contact manifolds, and Carnot group of step 2.</p>
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Pointwise Schauder Estimates of Parabolic Equations in Carnot Groups
… layer of the Lie algebra stratification for a Carnot group. The Schauder estimates are shown by means of Campanato spaces. These spaces make the pointwise nature of the estimates possible by comparing solutions to their Taylor polynomials. As a prerequisite device, a version of both the mean …
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Maximum principle, mean value operators and quasi boundedness in non-euclidean settings
… vector fields in RN, generating metric spaces of Carnot- Carath´eodory type. The Carnot-Carath´eodory metric related to a family {Xj}j=1,...,m is the control distance obtained by minimizing the time needed to go from two points along piecewise trajectories of vector fields. We are mainly …
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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
… geometry, with a special focus on the Heisenberg group Hn, Heisenbergtype (H-type) groups, and Carnot groups.</p> <p>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, …
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New Characterizations Of Sobolev Spaces On Heisenberg And Carnot Groups And High Order Sobolev Spaces On Eucliean Spaces
… in-depth study of Sobolev spaces on Heisenberg groups, as well as Carnot groups, second order and high order Sobolev spaces on Euclidean spaces.</p>