Tubular neighborhoods of nodal sets and diophantine approximation

Dmitry Jakobson; Dan Mangoubi

doi:10.1353/ajm.0.0066

Tubular neighborhoods of nodal sets and diophantine approximation

Dmitry Jakobson^*, Dan Mangoubi

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

6 Scopus citations

Abstract

We give upper and lower bounds on the volume of a tubular neighborhood of the nodal set of an eigenfunction of the Laplacian on a real analytic closed Riemannian manifold M. As an application we consider the question of approximating points on M by nodal sets, and explore analogy with approximation by rational numbers..

Original language	English
Pages (from-to)	1109-1135
Number of pages	27
Journal	American Journal of Mathematics
Volume	131
Issue number	4
DOIs	https://doi.org/10.1353/ajm.0.0066
State	Published - Aug 2009
Externally published	Yes

Access to Document

10.1353/ajm.0.0066

Cite this

@article{5eee5ad27e7a4c6ebd438b03b64501b8,

title = "Tubular neighborhoods of nodal sets and diophantine approximation",

abstract = "We give upper and lower bounds on the volume of a tubular neighborhood of the nodal set of an eigenfunction of the Laplacian on a real analytic closed Riemannian manifold M. As an application we consider the question of approximating points on M by nodal sets, and explore analogy with approximation by rational numbers..",

author = "Dmitry Jakobson and Dan Mangoubi",

year = "2009",

month = aug,

doi = "10.1353/ajm.0.0066",

language = "אנגלית",

volume = "131",

pages = "1109--1135",

journal = "American Journal of Mathematics",

issn = "0002-9327",

publisher = "Johns Hopkins University Press",

number = "4",

}

TY - JOUR

T1 - Tubular neighborhoods of nodal sets and diophantine approximation

AU - Jakobson, Dmitry

AU - Mangoubi, Dan

PY - 2009/8

Y1 - 2009/8

N2 - We give upper and lower bounds on the volume of a tubular neighborhood of the nodal set of an eigenfunction of the Laplacian on a real analytic closed Riemannian manifold M. As an application we consider the question of approximating points on M by nodal sets, and explore analogy with approximation by rational numbers..

AB - We give upper and lower bounds on the volume of a tubular neighborhood of the nodal set of an eigenfunction of the Laplacian on a real analytic closed Riemannian manifold M. As an application we consider the question of approximating points on M by nodal sets, and explore analogy with approximation by rational numbers..

UR - http://www.scopus.com/inward/record.url?scp=70450252328&partnerID=8YFLogxK

U2 - 10.1353/ajm.0.0066

DO - 10.1353/ajm.0.0066

M3 - ???researchoutput.researchoutputtypes.contributiontojournal.article???

AN - SCOPUS:70450252328

SN - 0002-9327

VL - 131

SP - 1109

EP - 1135

JO - American Journal of Mathematics

JF - American Journal of Mathematics

IS - 4

ER -

Tubular neighborhoods of nodal sets and diophantine approximation

Abstract

Access to Document

Other files and links

Fingerprint

Cite this