<?xml version="1.0" encoding="utf-8"?>
<TEI xmlns="http://www.tei-c.org/ns/1.0" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xmlns:hal="http://hal.archives-ouvertes.fr/" xmlns:gml="http://www.opengis.net/gml/3.3/" xmlns:gmlce="http://www.opengis.net/gml/3.3/ce" version="1.1" xsi:schemaLocation="http://www.tei-c.org/ns/1.0 http://api.archives-ouvertes.fr/documents/aofr-sword.xsd">
  <teiHeader>
    <fileDesc>
      <titleStmt>
        <title>HAL TEI export of hal-03268574v1</title>
      </titleStmt>
      <publicationStmt>
        <distributor>CCSD</distributor>
        <availability status="restricted">
          <licence target="https://creativecommons.org/publicdomain/zero/1.0/">CC0 1.0 - Universal</licence>
        </availability>
        <date when="2026-05-16T11:24:14+02:00"/>
      </publicationStmt>
      <sourceDesc>
        <p part="N">HAL API Platform</p>
      </sourceDesc>
    </fileDesc>
  </teiHeader>
  <text>
    <body>
      <listBibl>
        <biblFull>
          <titleStmt>
            <title xml:lang="en">Small eigenvalues of the rough and Hodge Laplacians under fixed volume</title>
            <author role="aut">
              <persName>
                <forename type="first">Colette</forename>
                <surname>Anné</surname>
              </persName>
              <idno type="halauthorid">127898-0</idno>
              <affiliation ref="#struct-37"/>
            </author>
            <author role="aut">
              <persName>
                <forename type="first">Junya</forename>
                <surname>Takahashi</surname>
              </persName>
              <idno type="halauthorid">321676-0</idno>
              <affiliation ref="#struct-463617"/>
            </author>
            <editor role="depositor">
              <persName>
                <forename>Colette</forename>
                <surname>Anné</surname>
              </persName>
              <email type="md5">c1e8cf42314e9c44525a18b032ca4da3</email>
              <email type="domain">univ-nantes.fr</email>
            </editor>
          </titleStmt>
          <editionStmt>
            <edition n="v1" type="current">
              <date type="whenSubmitted">2021-06-23 12:14:10</date>
              <date type="whenModified">2026-01-15 16:34:03</date>
              <date type="whenReleased">2021-06-24 10:11:33</date>
              <date type="whenProduced">2021-06-23</date>
              <date type="whenEndEmbargoed">2021-06-23</date>
              <ref type="file" target="https://hal.science/hal-03268574v1/document">
                <date notBefore="2021-06-23"/>
              </ref>
              <ref type="file" subtype="author" n="1" target="https://hal.science/hal-03268574v1/file/small-vol.pdf" id="file-3268574-2872148">
                <date notBefore="2021-06-23"/>
              </ref>
              <ref type="externalLink" target="http://arxiv.org/pdf/2106.12814"/>
            </edition>
            <edition n="v2">
              <date type="whenSubmitted">2022-03-09 15:26:08</date>
            </edition>
            <respStmt>
              <resp>contributor</resp>
              <name key="117644">
                <persName>
                  <forename>Colette</forename>
                  <surname>Anné</surname>
                </persName>
                <email type="md5">c1e8cf42314e9c44525a18b032ca4da3</email>
                <email type="domain">univ-nantes.fr</email>
              </name>
            </respStmt>
          </editionStmt>
          <publicationStmt>
            <distributor>CCSD</distributor>
            <idno type="halId">hal-03268574</idno>
            <idno type="halUri">https://hal.science/hal-03268574</idno>
            <idno type="halBibtex">anne:hal-03268574</idno>
            <idno type="halRefHtml">2021</idno>
            <idno type="halRef">2021</idno>
            <availability status="restricted">
              <licence target="https://about.hal.science/hal-authorisation-v1/">HAL Authorization<ref corresp="#file-3268574-2872148"/></licence>
            </availability>
          </publicationStmt>
          <seriesStmt/>
          <notesStmt/>
          <sourceDesc>
            <biblStruct>
              <analytic>
                <title xml:lang="en">Small eigenvalues of the rough and Hodge Laplacians under fixed volume</title>
                <author role="aut">
                  <persName>
                    <forename type="first">Colette</forename>
                    <surname>Anné</surname>
                  </persName>
                  <idno type="halauthorid">127898-0</idno>
                  <affiliation ref="#struct-37"/>
                </author>
                <author role="aut">
                  <persName>
                    <forename type="first">Junya</forename>
                    <surname>Takahashi</surname>
                  </persName>
                  <idno type="halauthorid">321676-0</idno>
                  <affiliation ref="#struct-463617"/>
                </author>
              </analytic>
              <monogr>
                <imprint/>
              </monogr>
              <idno type="arxiv">2106.12814</idno>
            </biblStruct>
          </sourceDesc>
          <profileDesc>
            <langUsage>
              <language ident="en">English</language>
            </langUsage>
            <textClass>
              <classCode scheme="halDomain" n="math.math-sp">Mathematics [math]/Spectral Theory [math.SP]</classCode>
              <classCode scheme="halDomain" n="math.math-dg">Mathematics [math]/Differential Geometry [math.DG]</classCode>
              <classCode scheme="halTypology" n="UNDEFINED">Preprints, Working Papers, ...</classCode>
              <classCode scheme="halOldTypology" n="UNDEFINED">Preprints, Working Papers, ...</classCode>
              <classCode scheme="halTreeTypology" n="UNDEFINED">Preprints, Working Papers, ...</classCode>
            </textClass>
            <abstract xml:lang="en">
              <p>For each degree p, we construct on any closed manifold a family of Riemannian metrics, with fixed volume such that any positive eigenvalues of the rough and Hodge Laplacians acting on differential p-forms converge to zero. In particular, on the sphere, we can choose these Riemannian metrics as those of non-negative sectional curvature. This is a generalization of the results by Colbois and Maerten in 2010 to the case of higher degree forms.</p>
            </abstract>
          </profileDesc>
        </biblFull>
      </listBibl>
    </body>
    <back>
      <listOrg type="structures">
        <org type="laboratory" xml:id="struct-37" status="OLD">
          <idno type="IdRef">087220865</idno>
          <idno type="ISNI">0000000097740814</idno>
          <idno type="RNSR">199612400A</idno>
          <orgName>Laboratoire de Mathématiques Jean Leray</orgName>
          <orgName type="acronym">LMJL</orgName>
          <date type="end">2021-12-31</date>
          <desc>
            <address>
              <country key="FR"/>
            </address>
            <ref type="url">http://www.math.sciences.univ-nantes.fr/jeanleray/</ref>
          </desc>
          <listRelation>
            <relation active="#struct-97058" type="direct"/>
            <relation active="#struct-93263" type="indirect"/>
            <relation name="UMR6629" active="#struct-441569" type="direct"/>
          </listRelation>
        </org>
        <org type="regrouplaboratory" xml:id="struct-463617" status="VALID">
          <orgName>Research Center for Pure and Applied Mathematics [Tohoku University]</orgName>
          <desc>
            <address>
              <addrLine>Division of Mathematics &amp; Research Center for Pure and Applied Mathematics Graduate School of Information Sciences Tohoku University 6-3-09 Aramaki-Aza-Aoba, Aoba-ku, Sendai 980-8579, Japan</addrLine>
              <country key="JP"/>
            </address>
            <ref type="url">https://www.math.is.tohoku.ac.jp/english/research/</ref>
          </desc>
          <listRelation>
            <relation active="#struct-206219" type="direct"/>
            <relation active="#struct-311564" type="indirect"/>
          </listRelation>
        </org>
        <org type="regrouplaboratory" xml:id="struct-97058" status="OLD">
          <orgName>Université de Nantes - UFR des Sciences et des Techniques</orgName>
          <orgName type="acronym">UN UFR ST</orgName>
          <date type="end">2021-12-31</date>
          <desc>
            <address>
              <addrLine>2, rue de la Houssinière - BP 92208 - 44322 Nantes cedex 3</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">http://www.sciences-techniques.univ-nantes.fr/</ref>
          </desc>
          <listRelation>
            <relation active="#struct-93263" type="direct"/>
          </listRelation>
        </org>
        <org type="institution" xml:id="struct-93263" status="OLD">
          <idno type="IdRef">026403447</idno>
          <idno type="ROR">https://ror.org/03gnr7b55</idno>
          <orgName>Université de Nantes</orgName>
          <orgName type="acronym">UN</orgName>
          <date type="end">2021-12-31</date>
          <desc>
            <address>
              <addrLine>1, quai de Tourville - BP 13522 - 44035 Nantes cedex 1</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">http://www.univ-nantes.fr/</ref>
          </desc>
        </org>
        <org type="regroupinstitution" xml:id="struct-441569" status="VALID">
          <idno type="IdRef">02636817X</idno>
          <idno type="ISNI">0000000122597504</idno>
          <idno type="ROR">https://ror.org/02feahw73</idno>
          <orgName>Centre National de la Recherche Scientifique</orgName>
          <orgName type="acronym">CNRS</orgName>
          <date type="start">1939-10-19</date>
          <desc>
            <address>
              <country key="FR"/>
            </address>
            <ref type="url">https://www.cnrs.fr/</ref>
          </desc>
        </org>
        <org type="institution" xml:id="struct-206219" status="VALID">
          <orgName>Graduate School of Information Sciences [Tohoku University]</orgName>
          <desc>
            <address>
              <addrLine>Aoba Ward, Sendai, Miyagi 980-0845</addrLine>
              <country key="JP"/>
            </address>
            <ref type="url">https://www.is.tohoku.ac.jp/en/</ref>
          </desc>
          <listRelation>
            <relation active="#struct-311564" type="direct"/>
          </listRelation>
        </org>
        <org type="regroupinstitution" xml:id="struct-311564" status="VALID">
          <idno type="ROR">https://ror.org/01dq60k83</idno>
          <orgName>Tohoku University [Sendai]</orgName>
          <desc>
            <address>
              <addrLine>2-1-1 Katahira, Aoba-ku, Sendai, 980-8577 Japan</addrLine>
              <country key="JP"/>
            </address>
            <ref type="url">https://www.tohoku.ac.jp/en/</ref>
          </desc>
        </org>
      </listOrg>
    </back>
  </text>
</TEI>