Intersections of projections and slicing theorems for the isotropic Grassmannian and the Heisenberg group

DOI10.1515/agms-2020-0002zbMath1436.28003arXiv1907.07218OpenAlexW3009589109MaRDI QIDQ1987314

Fernando Román-García

Publication date: 14 April 2020

Published in: Analysis and Geometry in Metric Spaces (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1907.07218

zbMATH Keywords

integral geometryorthogonal projectionsintersection of planes and setsisotropic Grassmanian

Mathematics Subject Classification ID

Length, area, volume, other geometric measure theory (28A75) Hausdorff and packing measures (28A78)

Cites Work

• Projection and slicing theorems in Heisenberg groups
• Transversality of isotropic projections, unrectifiability, and Heisenberg groups
• An introduction to the Heisenberg group and the sub-Riemannian isoperimetric problem
• The effect of projections on dimension in the Heisenberg group
• Smoothness of projections, Bernoulli convolutions, and the dimension of exceptions
• Improved Hausdorff dimension estimate for vertical projections in the Heisenberg group
• Hausdorff dimension, intersections of projections and exceptional plane sections
• Characterizations of intrinsic rectifiability in Heisenberg groups
• Hausdorff dimension, orthogonal projections and intersections with planes
• Measure and dimension functions: measurability and densities
• Fourier Analysis and Hausdorff Dimension
• On Hausdorff dimension of projections
• The (φ, k) Rectifiable Subsets of n Space
• Some Fundamental Geometrical Properties of Plane Sets of Fractional Dimensions
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