Valuations on manifolds and Rumin cohomology

By A. Bernig, L. Bröcker. 2007

101 citations recorded by the source corpus.

Subfields: Applied Mathematics, Computational Theory and Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/91029c6739d29b3abc68b76087719b14026db256

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In Applied Mathematics

In Computational Theory and Mathematics

In Geometry and Topology

Citations in the corpus

$\mathrm{GL}(n)$ contravariant Minkowski valuations (2012, unknown): “, [1–5, 7, 15–17, 19, 22].”
Valuations on Sobolev spaces (2012, background): “Valuations were also investigated on star shaped sets [27, 28], on manifolds [6, 7, 8, 10, 11] and on Lebesgue spaces [37, 56, 57].”
The module of unitarily invariant area measures (2012, methodology): “The kernel of the map Ωn−1(SV )tr → Valsm given by integration with respect to the normal cycle was determined by Bernig and Bröcker [19] using the Rumin differential operator.”
Minkowski valuations intertwining the special linear group (2012, unknown): “, [5–7,9,10,12–14,31,32,63]).”
Integral geometry of complex space forms (2012, background): “By [17] this is equivalent to Dλω = π∗ vol.”
The product on smooth and generalized valuations (2009, methodology): “[16] The smooth valuation represented by (ω,φ)∈Ωn−1(PX)× Ωn(X) is trivial if and only if Dω+π∗φ= 0; (3) π∗ω = 0.”
Hermitian integral geometry (2008, methodology): “The kernel of the map Ψ of (15) has been characterized in [12].”
Harmonic Analysis of Translation Invariant Valuations (2010, methodology): “3 was the main tool used in [14] to establish a Hard Lefschetz Theorem for translation invariant valuations (see also [6, 9]).”
Projection bodies in complex vector spaces (2011, background): “The classical case A = R has attracted a lot of attention, we refer to [1, 2, 3, 4, 7, 8, 13, 20, 29] for some new developments.”
Minkowski valuations and generalized valuations (2015, methodology): “For example, the following Hard Lefschetz type theorem for the operator Λ was proved by Alesker [5] for even and by Bernig and Bröcker [14] for general valuations.”
Fisher information and matrix-valued valuations (2011, background): “Valuations were also investigated on star shaped sets [25,26] and on manifolds [6–8,10].”
A fourier-type transform on translation-invariant valuations on convex sets (2007, methodology): “As an application of the Fourier transform (combined with Bernig-Bröcker theorem [14]) we prove a version of hard Lefschetz theorem for valuations.”