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Rectifiability in Carnot Groups [PDF]
, 2022 This thesis is devoted to the study of the theory of rectifiability of sets and measures in the non smooth context of Carnot groups. The focus is on the study of the notion of P-rectifiability and its relation with other notions of rectifiability in Carnot groups.
ANTONELLI, GIOACCHINO
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Intrinsic regular surfaces in Carnot groups
Bruno Pini Mathematical Analysis SeminarA Carnot group $G$ is a simply connected, nilpotent Lie group with stratified Lie algebra. Intrinsic regular surfaces in Carnot groups play the same role as C1 surfaces in Euclidean spaces.
Daniela Di Donato
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Curvature exponent and geodesic dimension on Sard-regular Carnot groups
Analysis and Geometry in Metric SpacesIn this study, we characterize the geodesic dimension NGEO{N}_{{\rm{GEO}}} and give a new lower bound to the curvature exponent NCE{N}_{{\rm{CE}}} on Sard-regular Carnot groups.
Golo Sebastiano Nicolussi, Zhang Ye
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Geodesics in the Heisenberg Group
Analysis and Geometry in Metric Spaces, 2015 We provide a new and elementary proof for the structure of geodesics in the Heisenberg group Hn. The proof is based on a new isoperimetric inequality for closed curves in R2n.We also prove that the Carnot- Carathéodory metric is real analytic away from ...
Hajłasz Piotr, Zimmerman Scott
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Analysis and Geometry in Metric Spaces, 2013 In this paper we study heat kernels associated with a Carnot group G, endowed with a family of collapsing left-invariant Riemannian metrics σε which converge in the Gromov- Hausdorff sense to a sub-Riemannian structure on G as ε→ 0.
Capogna Luca +2 more
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Frontiers in Physics, 2021 Solitons are coherent structures that describe the nonlinear evolution of wave localizations in hydrodynamics, optics, plasma and Bose-Einstein condensates.
Amin Chabchoub +12 more
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Subelliptic and parametric equations on Carnot groups [PDF]
Proceedings of the American Mathematical Society, 2015 This article concerns a class of elliptic equations on Carnot groups depending on one real parameter. Our approach is based on variational methods. More precisely, we establish the existence of at least two weak solutions for the treated problem by using a direct consequence of the celebrated Pucci-Serrin theorem and of a local minimum result for ...
Molica Bisci G, Ferrara M
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On Rectifiable Measures in Carnot Groups: Existence of Density
The Journal of Geometric Analysis, 2022 AbstractIn this paper, we start a detailed study of a new notion of rectifiability in Carnot groups: we say that a Radon measure is$${\mathscr {P}}_h$$Ph-rectifiable, for$$h\in {\mathbb {N}}$$h∈N, if it has positiveh-lower density and finiteh-upper density almost everywhere, and, at almost every point, it admits a unique tangent measure up to multiples.
Gioacchino Antonelli, Andrea Merlo
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APPROXIMATIONS OF SOBOLEV NORMS IN CARNOT GROUPS [PDF]
Communications in Contemporary Mathematics, 2011 This paper deals with a notion of Sobolev space W1, pintroduced by Bourgain, Brezis and Mironescu by means of a seminorm involving local averages of finite differences. This seminorm was subsequently used by Ponce to obtain a Poincaré-type inequality.
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Functional properties of limits of Sobolev homeomorphisms with integrable distortion
Современная математика: Фундаментальные направленияThe functional and geometric properties of limits of homeomorphisms with integrable distortion of domains in Carnot groups are studied. The homeomorphisms belong to Sobolev classes.
S. K. Vodopyanov, S. V. Pavlov
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