Density problems on vector bundles and manifolds

Bandara, Lashi

doi:10.1090/s0002-9939-2014-12284-2

Cited by 18 publications

(25 citation statements)

References 10 publications

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“…1. If Ric ≥ −C for some C ≥ 0, then M satisfies the L 2 -Calderon-Zygmund inequality, with C 2 = 1, D 2 = C, thus in case q = 2, we recover Theorem 1.1 in [2] within the class of of M's with nonnegative Ricci curvature (noting that the proof of Theorem 1.1 in [2] heavily relies on Hilbert space arguments and thus does not extend directly to general q's). We refer the reader to the monograph [14] for results into this direction on the whole L q -scale.…”

Section: Denseness Of Cmentioning

confidence: 84%

Sequences of Laplacian Cut-Off Functions

Güneysu

2014

J Geom Anal

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Abstract. We derive several new applications of the concept of sequences of Laplacian cut-off functions on Riemannian manifolds (which we prove to exist on geodesically complete Riemannian manifolds with nonnegative Ricci curvature): In particular, we prove that this existence implies L q -estimates of the gradient, a new density result of smooth compactly supported functions in Sobolev spaces on the whole L q -scale, and a slightly weaker and slightly stronger variant of the conjecture of Braverman, Milatovic and Shubin on the nonnegativity of L 2 -solutions f of (−∆ + 1)f ≥ 0. The latter fact is proved within a new notion of positivity preservation for Riemannian manifolds which is related to stochastic completeness.

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Section: Denseness Of Cmentioning

confidence: 84%

Sequences of Laplacian Cut-Off Functions

Güneysu

2014

J Geom Anal

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“…Moreover, recall that the divergence operator is then div = −∇ 2 * . It is well known that C ∞ c (V) is dense in W 1,2 (V) and when g is smooth, that C ∞ c (T * M ⊗ V) is dense in D(div) (see [5]). In what is to follow, we will sometimes write ∇ in place of ∇ 2 .…”

Section: Manifolds and Vector Bundlesmentioning

confidence: 99%

Riesz continuity of the Atiyah–Singer Dirac operator under perturbations of the metric

Bandara¹,

McIntosh²,

Rosén³

2017

Math. Ann.

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“…By combining this with Theorem 1 of McIntosh and the author in [6], we obtain the following important corollary.…”

Section: 2mentioning

confidence: 65%

Rough metrics on manifolds and quadratic estimates

Bandara

2016

Math. Z.

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Abstract. We study the persistence of quadratic estimates related to the Kato square root problem across a change of metric on smooth manifolds by defining a class of Riemannian-like metrics that are permitted to be of low regularity and degenerate on sets of measure zero. We also demonstrate how to transmit quadratic estimates between manifolds which are homeomorphic and locally bi-Lipschitz. As a consequence, we demonstrate the invariance of the Kato square root problem under Lipschitz transformations of the space and obtain solutions to this problem on functions and forms on compact manifolds with a continuous metric. Furthermore, we show that a lower bound on the injectivity radius is not a necessary condition to solve the Kato square root problem.

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Density problems on vector bundles and manifolds

Cited by 18 publications

References 10 publications

Sequences of Laplacian Cut-Off Functions

Sequences of Laplacian Cut-Off Functions

Riesz continuity of the Atiyah–Singer Dirac operator under perturbations of the metric

Rough metrics on manifolds and quadratic estimates

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