Formes différentielles sur les variétés de contact

Rumin, Michel

doi:10.4310/jdg/1214454873

Cited by 195 publications

(269 citation statements)

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“…The differential operator D was introduced by Rumin [22] for an arbitrary contact manifold, and it depends only on the contact structure. In our case for any smooth manifold X the space P + (T * X) has a canonical contact structure, and the operator D used in the proof of Lemma 8.1.1 corresponds to it.…”

Section: Remarkmentioning

confidence: 99%

“…where D : C ∞ (P + (T * R n ), Ω n−1 ) → C ∞ (P + (T * R n ), Ω n ) is an explicitly written differential operator of second order (introduced by Rumin in [22]). However in the proof of the "if" part of Theorem 1 in [7] the authors used equality (8.1.8) not for the whole class of compact subanalytic sets, but for the subclass of compact subanalytic submanifolds with boundary.…”

Section: Imbedding Of Constructible Functions To Generalized Valuationsmentioning

confidence: 99%

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Theory of Valuations on Manifolds, IV. New Properties of the Multiplicative Structure

Alesker

Lecture Notes in Mathematics

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This is the fourth part in the series of articles [4], [5], [6] (see also [3]) where the theory of valuations on manifolds is developed. In this part it is shown that the filtration on valuations is compatible with the product. Then it is proved that the Euler-Verdier involution on smooth valuations is an automorphism of the algebra of valuations. Then an integration functional on valuations with compact support is introduced, and a property of selfduality of valuations is proved. Next a space of generalized valuations is defined, and some basic properties of it are proved. Finally a canonical imbedding of the space of constructible functions on a real analytic manifold into the space of generalized valuations is constructed, and various structures on valuations are compared with known structures on constructible functions.

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Section: Remarkmentioning

confidence: 99%

Section: Imbedding Of Constructible Functions To Generalized Valuationsmentioning

confidence: 99%

Theory of Valuations on Manifolds, IV. New Properties of the Multiplicative Structure

Alesker

Lecture Notes in Mathematics

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“…The harmonic theory on a closed Sasakian manifold has been extensively studied by many geometers (say, [4,7,15,22,23]). Some of these results have been extended to closed contact metric manifolds (say [19,20]). The harmonic theory developed before is usually founded on an adapted metric g ω defined by…”

Section: Introductionmentioning

confidence: 99%

Transversal Harmonic Theory for Transversally Symplectic Flows

Pak¹

2008

J. Aust. Math. Soc.

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“…Nevertheless, as it appears from our methods, the exponential decays we obtain are optimal but are mainly consequences of spectral properties, so that we do not really rely on any notion of intrinsic Ricci curvature excepted in the Li-Yau type estimate that we obtain. In the future, we hope to extend those methods to cover more general situations and to make the link with more geometrically oriented works like for instance [26], where a Bonnet-Myers type theorem is obtained in a hypoelliptic situation. So, finally, this work is mainly divided into two parts.…”

Section: Introductionmentioning

confidence: 99%