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Eigenvalue Comparison on Bakry-Emery Manifolds

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Andrews, Benjamin; Ni, Lei

Description

We prove a comparison theorem on the modulus of continuity of the solution of a heat equation with a drifting term on Bakry-Emery manifolds. A direct consequence of the result is an alternate proof of an eigenvalue comparison result of Bakry-Qian. Examples are given to show that the estimate is sharp. Discussions on an explicit lower estimate for the corresponding ODE and an application to the diameter lower bound for gradient shrinking solitons are also included.

dc.contributor.authorAndrews, Benjamin
dc.contributor.authorNi, Lei
dc.date.accessioned2015-12-07T22:17:54Z
dc.identifier.issn0360-5302
dc.identifier.urihttp://hdl.handle.net/1885/18791
dc.description.abstractWe prove a comparison theorem on the modulus of continuity of the solution of a heat equation with a drifting term on Bakry-Emery manifolds. A direct consequence of the result is an alternate proof of an eigenvalue comparison result of Bakry-Qian. Examples are given to show that the estimate is sharp. Discussions on an explicit lower estimate for the corresponding ODE and an application to the diameter lower bound for gradient shrinking solitons are also included.
dc.publisherMarcel Dekker Inc.
dc.sourceCommunications in Partial Differential Equations
dc.subjectKeywords: Bakry-Emery manifolds; Eigenvalue estimates; Harmonic oscillator; Heat equation; Modulus of continuity; Ricci solitons; Weber's equation
dc.titleEigenvalue Comparison on Bakry-Emery Manifolds
dc.typeJournal article
local.description.notesImported from ARIES
local.identifier.citationvolume37
dc.date.issued2012
local.identifier.absfor010110 - Partial Differential Equations
local.identifier.absfor010102 - Algebraic and Differential Geometry
local.identifier.ariespublicationu8610103xPUB5
local.type.statusPublished Version
local.contributor.affiliationAndrews, Benjamin, College of Physical and Mathematical Sciences, ANU
local.contributor.affiliationNi, Lei, University of California
local.bibliographicCitation.startpage2081
local.bibliographicCitation.lastpage2092
local.identifier.doi10.1080/03605302.2012.668602
local.identifier.absseo970101 - Expanding Knowledge in the Mathematical Sciences
dc.date.updated2016-02-24T11:40:46Z
local.identifier.scopusID2-s2.0-84867877078
local.identifier.thomsonID000310738700006
CollectionsANU Research Publications

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