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dc.contributor.authorLotoreichik, Vladimir
dc.contributor.authorOurmières-Bonafos, Thomas
dc.date.accessioned2019-04-17T12:46:40Z
dc.date.available2019-04-17T12:46:40Z
dc.date.issued2018
dc.identifier.urihttps://basepub.dauphine.fr/handle/123456789/18684
dc.language.isoenen
dc.subjectDirac operatoren
dc.subjectinfinite mass boundary conditionen
dc.subjectlowest eigenvalueen
dc.subjectshapeoptimizationen
dc.subject.ddc515en
dc.titleA sharp upper bound on the spectral gap for convex graphene quantum dotsen
dc.typeDocument de travail / Working paper
dc.description.abstractenThe main result of this paper is a sharp upper bound on the first positive eigenvalue of Dirac operators in two dimensional simply connected C3-domains with infinite mass boundary conditions. This bound is given in terms of a conformal variation, explicit geometric quantities and of the first eigenvalue for the disk. Its proof relies on the min-max principle applied to the squares of these Dirac operators. A suitable test function is constructed by means of a conformal map. This general upper bound involves the norm of the derivative of the underlying conformal map in the Hardy space H2(D). Then, we apply known estimates of this norm for convex and for nearly circular, star-shaped domains in order to get explicit geometric upper bounds on the eigenvalue. These bounds can be re-interpreted as reverse Faber-Krahn-type inequalities under adequate geometric constraints.en
dc.publisher.nameCahier de recherche CEREMADE, Université Paris-Dauphineen
dc.publisher.cityParisen
dc.identifier.citationpages26en
dc.relation.ispartofseriestitleCahier de recherche CEREMADE, Université Paris-Dauphineen
dc.subject.ddclabelAnalyseen
dc.identifier.citationdate2018
dc.description.ssrncandidatenonen
dc.description.halcandidatenonen
dc.description.readershiprechercheen
dc.description.audienceInternationalen
dc.date.updated2019-03-27T09:40:08Z
hal.person.labIds88672
hal.person.labIds60


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