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The spectrum of geodesic balls on spherically symmetric manifolds

The result's identifiers

  • Result code in IS VaVaI

    <a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F62690094%3A18470%2F17%3A50013788" target="_blank" >RIV/62690094:18470/17:50013788 - isvavai.cz</a>

  • Result on the web

    <a href="http://dx.doi.org/10.4310/CAG.2017.v25.n3.a1" target="_blank" >http://dx.doi.org/10.4310/CAG.2017.v25.n3.a1</a>

  • DOI - Digital Object Identifier

    <a href="http://dx.doi.org/10.4310/CAG.2017.v25.n3.a1" target="_blank" >10.4310/CAG.2017.v25.n3.a1</a>

Alternative languages

  • Result language

    angličtina

  • Original language name

    The spectrum of geodesic balls on spherically symmetric manifolds

  • Original language description

    We study the Dirichlet spectrum of the Laplace operator on geodesic balls centred at a pole of spherically symmetric manifolds. We first derive a Hadamard-type formula for the dependence of the first eigenvalue lambda(1) on the radius r of the ball, which allows us to obtain lower and upper bounds for.1 in specific cases. For the sphere and hyperbolic space, these bounds are asymptotically sharp as r approaches zero and we see that while in two dimensions lambda(1) is bounded from above by the first two terms in the asymptotics for small r, for dimensions four and higher the reverse inequality holds. In the general case we derive the asymptotic expansion of lambda(1) for small radius and determine the first three terms explicitly. For compact manifolds we carry out similar calculations as the radius of the geodesic ball approaches the diameter of the manifold. In the latter case we show that in even dimensions there will always exist logarithmic terms in these expansions.

  • Czech name

  • Czech description

Classification

  • Type

    J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database

  • CEP classification

  • OECD FORD branch

    10101 - Pure mathematics

Result continuities

  • Project

  • Continuities

    I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Others

  • Publication year

    2017

  • Confidentiality

    S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Data specific for result type

  • Name of the periodical

    COMMUNICATIONS IN ANALYSIS AND GEOMETRY

  • ISSN

    1019-8385

  • e-ISSN

  • Volume of the periodical

    25

  • Issue of the periodical within the volume

    3

  • Country of publishing house

    US - UNITED STATES

  • Number of pages

    38

  • Pages from-to

    507-544

  • UT code for WoS article

    000410554400001

  • EID of the result in the Scopus database