Contact integral geometry and the Heisenberg algebra

DOI10.2140/gt.2019.23.3041zbMath1432.53107arXiv1712.09313OpenAlexW3100564391WikidataQ126626432 ScholiaQ126626432MaRDI QIDQ2279150

Dmitry Faifman

Publication date: 12 December 2019

Published in: Geometry \& Topology (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1712.09313

zbMATH Keywords

Heisenberg algebracontact manifoldintrinsic volumesCrofton formulaWeyl principleLipschitz Killing curvatures

Mathematics Subject Classification ID

Symplectic manifolds (general theory) (53D05) Integral geometry (53C65) Contact manifolds (general theory) (53D10) Mixed volumes and related topics in convex geometry (52A39) Dissections and valuations (Hilbert's third problem, etc.) (52B45) Almost contact and almost symplectic manifolds (53D15) Differential invariants (local theory), geometric objects (53A55)

Related Items (6)

Classification of angular curvature measures and a proof of the angularity conjecture ⋮ The Weyl principle on the Finsler frontier ⋮ Curvature measures of pseudo-Riemannian manifolds ⋮ Uniqueness of curvature measures in pseudo-Riemannian geometry ⋮ On mixed Hodge–Riemann relations for translation-invariant valuations and Aleksandrov–Fenchel inequalities ⋮ From harmonic analysis of translation-invariant valuations to geometric inequalities for convex bodies

Cites Work

• Unnamed Item
• Unnamed Item
• Asymptotic equivalence of symplectic capacities
• Isosystolic inequalities for optical hypersurfaces
• Spin-invariant valuations on the octonionic plane
• Algebraic/combinatorial proofs of Cayley-type identities for derivatives of determinants and Pfaffians
• Classification of invariant valuations on the quaternionic plane
• Integral geometry and valuations. Notes of the lectures given in the advanced course on integral geometry and valuation theory, Barcelona, Spain, September 6--10, 2010. Edited by Eduardo Gallego and Gil Solanes
• A systolic inequality for geodesic flows on the two-sphere
• \(\mathrm{SL}(n)\) invariant valuations on polytopes
• Valuations on manifolds and integral geometry
• Hermitian integral geometry
• From symplectic measurements to the Mahler conjecture
• Theory of valuations on manifolds. II
• Vector fields in the presence of a contact structure
• Invariant functionals on Speh representations
• A product formula for valuations on manifolds with applications to the integral geometry of the quaternionic line
• Heat equation and the volume of tubes
• The second fundamental form of a plane field
• Differential forms on contact manifolds
• Lagrangians satisfying Crofton formulas, Radon transforms, and nonlocal differentials
• Projections of convex bodies and the Fourier transform
• The multiplicative structure on continuous polynomial valuations
• On the transverse symbol of vectorial distributions and some applications to harmonic analysis
• An extension of Schäffer's dual girth conjecture to Grassmannians
• A characterization of affine surface area
• Valuation theory of indefinite orthogonal groups
• Crofton formulas and indefinite signature
• The tangent groupoid of a Heisenberg manifold
• The M-ellipsoid, symplectic capacities and volume
• Integral geometry of complex space forms
• Contact geometry and isosystolic inequalities
• Theory of valuations on manifolds. I: Linear spaces
• Convex valuations invariant under the Lorentz group
• The product on smooth and generalized valuations
• Heisenberg calculus and spectral theory of hypoelliptic operators on Heisenberg manifolds
• Valuations and Euler-Type Relations on Certain Classes of Convex Polytopes
• Singular invariant hyperfunctions on the square matrix space and the alternating matrix space
• Even valuations on convex bodies
• Metric and isoperimetric problems in symplectic geometry
• Kinematic formulas on the quaternionic plane
• Convex Bodies The Brunn-MinkowskiTheory
• Theory of Valuations on Manifolds, IV. New Properties of the Multiplicative Structure
• Theory of valuations on manifolds, III. Multiplicative structure in the general case
• Dual spheres have the same girth
• Description of translation invariant valuations on convex sets with solution of P. McMullen's conjecture

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