An exhaustion of locally symmetric spaces by compact submanifolds with corners
Identifieur interne : 001C83 ( Main/Exploration ); précédent : 001C82; suivant : 001C84An exhaustion of locally symmetric spaces by compact submanifolds with corners
Auteurs : Enrico Leuzinger [Suisse]Source :
- Inventiones mathematicae [ 0020-9910 ] ; 1995-12-01.
English descriptors
- KwdEn :
- Appendice sect, Arithmetic group, Arithmetic groups, Asymptotic, Borel, Busemann, Busemann function, Busemann functions, Comer, Compact manifold, Compact submanifold, Compact submanifolds, Compact subset, Complete proofs, Equivalence classes, Exhaustion, Exhaustion function, Finite volume, Fundamental domains, Geodesic, Geodesic rays, Horocyclic projection, Horospheres, Identity component, Infinity, Isometry, Isotropy group, Lattice, Lemma, Leuzinger, Level sets, Maximal, Minimal parabolic group, Next lemma, Noncompact, Noncompact type, Nonpositive curvature, Open neighbourhood, Parabolic, Quotient, Raghunathan, Reduction theory, Resp, Riemannian, Sect, Siegel, Subgroup, Sublevel, Sublevel sets, Submanifold, Subset, Symmetric, Symmetric quotient, Symmetric space, Symmetric spaces.
- Teeft :
- Appendice sect, Arithmetic group, Arithmetic groups, Asymptotic, Borel, Busemann, Busemann function, Busemann functions, Comer, Compact manifold, Compact submanifold, Compact submanifolds, Compact subset, Complete proofs, Equivalence classes, Exhaustion, Exhaustion function, Finite volume, Fundamental domains, Geodesic, Geodesic rays, Horocyclic projection, Horospheres, Identity component, Infinity, Isometry, Isotropy group, Lattice, Lemma, Leuzinger, Level sets, Maximal, Minimal parabolic group, Next lemma, Noncompact, Noncompact type, Nonpositive curvature, Open neighbourhood, Parabolic, Quotient, Raghunathan, Reduction theory, Resp, Riemannian, Sect, Siegel, Subgroup, Sublevel, Sublevel sets, Submanifold, Subset, Symmetric, Symmetric quotient, Symmetric space, Symmetric spaces.
Abstract
Abstract: LetX be a Riemannian symmetric space of noncompact type and rank≧2 and let Γ be a non-uniform, irreducible lattice. On the locally symmetric quotientV=Γ/X we construct an exhaustion functionh:V→[0,∞) whose sublevel sets {h≦s} are compact submanifolds ofV with corners. The top dimensional boundary faces of {h≦s} are parts of certain horospheres that join together at the corners. It can be shown that actually {h≦s} is a submanifold with corners isomorphic to the Borel-Serre compactification ofV.
Url:
DOI: 10.1007/BF01884305
Affiliations:
Links toward previous steps (curation, corpus...)
- to stream Istex, to step Corpus: 000A81
- to stream Istex, to step Curation: 000A81
- to stream Istex, to step Checkpoint: 001A88
- to stream Main, to step Merge: 001D07
- to stream Main, to step Curation: 001C83
Le document en format XML
<record><TEI wicri:istexFullTextTei="biblStruct"><teiHeader><fileDesc><titleStmt><title xml:lang="en">An exhaustion of locally symmetric spaces by compact submanifolds with corners</title>
<author><name sortKey="Leuzinger, Enrico" sort="Leuzinger, Enrico" uniqKey="Leuzinger E" first="Enrico" last="Leuzinger">Enrico Leuzinger</name>
</author>
</titleStmt>
<publicationStmt><idno type="wicri:source">ISTEX</idno>
<idno type="RBID">ISTEX:33E2AF6547032913962C5A43884843D20BC7051E</idno>
<date when="1995" year="1995">1995</date>
<idno type="doi">10.1007/BF01884305</idno>
<idno type="url">https://api.istex.fr/document/33E2AF6547032913962C5A43884843D20BC7051E/fulltext/pdf</idno>
<idno type="wicri:Area/Istex/Corpus">000A81</idno>
<idno type="wicri:explorRef" wicri:stream="Istex" wicri:step="Corpus" wicri:corpus="ISTEX">000A81</idno>
<idno type="wicri:Area/Istex/Curation">000A81</idno>
<idno type="wicri:Area/Istex/Checkpoint">001A88</idno>
<idno type="wicri:explorRef" wicri:stream="Istex" wicri:step="Checkpoint">001A88</idno>
<idno type="wicri:doubleKey">0020-9910:1995:Leuzinger E:an:exhaustion:of</idno>
<idno type="wicri:Area/Main/Merge">001D07</idno>
<idno type="wicri:Area/Main/Curation">001C83</idno>
<idno type="wicri:Area/Main/Exploration">001C83</idno>
</publicationStmt>
<sourceDesc><biblStruct><analytic><title level="a" type="main" xml:lang="en">An exhaustion of locally symmetric spaces by compact submanifolds with corners</title>
<author><name sortKey="Leuzinger, Enrico" sort="Leuzinger, Enrico" uniqKey="Leuzinger E" first="Enrico" last="Leuzinger">Enrico Leuzinger</name>
<affiliation wicri:level="3"><country xml:lang="fr">Suisse</country>
<wicri:regionArea>Mathematisches Institut der Universität Zürich, Winterthurerstr. 190, CH-8057, Zürich</wicri:regionArea>
<placeName><settlement type="city">Zurich</settlement>
<region nuts="3" type="region">Canton de Zurich</region>
</placeName>
</affiliation>
<affiliation wicri:level="1"><country wicri:rule="url">Suisse</country>
</affiliation>
</author>
</analytic>
<monogr></monogr>
<series><title level="j">Inventiones mathematicae</title>
<title level="j" type="abbrev">Invent Math</title>
<idno type="ISSN">0020-9910</idno>
<idno type="eISSN">1432-1297</idno>
<imprint><publisher>Springer-Verlag</publisher>
<pubPlace>Berlin/Heidelberg</pubPlace>
<date type="published" when="1995-12-01">1995-12-01</date>
<biblScope unit="volume">121</biblScope>
<biblScope unit="issue">1</biblScope>
<biblScope unit="page" from="389">389</biblScope>
<biblScope unit="page" to="410">410</biblScope>
</imprint>
<idno type="ISSN">0020-9910</idno>
</series>
</biblStruct>
</sourceDesc>
<seriesStmt><idno type="ISSN">0020-9910</idno>
</seriesStmt>
</fileDesc>
<profileDesc><textClass><keywords scheme="KwdEn" xml:lang="en"><term>Appendice sect</term>
<term>Arithmetic group</term>
<term>Arithmetic groups</term>
<term>Asymptotic</term>
<term>Borel</term>
<term>Busemann</term>
<term>Busemann function</term>
<term>Busemann functions</term>
<term>Comer</term>
<term>Compact manifold</term>
<term>Compact submanifold</term>
<term>Compact submanifolds</term>
<term>Compact subset</term>
<term>Complete proofs</term>
<term>Equivalence classes</term>
<term>Exhaustion</term>
<term>Exhaustion function</term>
<term>Finite volume</term>
<term>Fundamental domains</term>
<term>Geodesic</term>
<term>Geodesic rays</term>
<term>Horocyclic projection</term>
<term>Horospheres</term>
<term>Identity component</term>
<term>Infinity</term>
<term>Isometry</term>
<term>Isotropy group</term>
<term>Lattice</term>
<term>Lemma</term>
<term>Leuzinger</term>
<term>Level sets</term>
<term>Maximal</term>
<term>Minimal parabolic group</term>
<term>Next lemma</term>
<term>Noncompact</term>
<term>Noncompact type</term>
<term>Nonpositive curvature</term>
<term>Open neighbourhood</term>
<term>Parabolic</term>
<term>Quotient</term>
<term>Raghunathan</term>
<term>Reduction theory</term>
<term>Resp</term>
<term>Riemannian</term>
<term>Sect</term>
<term>Siegel</term>
<term>Subgroup</term>
<term>Sublevel</term>
<term>Sublevel sets</term>
<term>Submanifold</term>
<term>Subset</term>
<term>Symmetric</term>
<term>Symmetric quotient</term>
<term>Symmetric space</term>
<term>Symmetric spaces</term>
</keywords>
<keywords scheme="Teeft" xml:lang="en"><term>Appendice sect</term>
<term>Arithmetic group</term>
<term>Arithmetic groups</term>
<term>Asymptotic</term>
<term>Borel</term>
<term>Busemann</term>
<term>Busemann function</term>
<term>Busemann functions</term>
<term>Comer</term>
<term>Compact manifold</term>
<term>Compact submanifold</term>
<term>Compact submanifolds</term>
<term>Compact subset</term>
<term>Complete proofs</term>
<term>Equivalence classes</term>
<term>Exhaustion</term>
<term>Exhaustion function</term>
<term>Finite volume</term>
<term>Fundamental domains</term>
<term>Geodesic</term>
<term>Geodesic rays</term>
<term>Horocyclic projection</term>
<term>Horospheres</term>
<term>Identity component</term>
<term>Infinity</term>
<term>Isometry</term>
<term>Isotropy group</term>
<term>Lattice</term>
<term>Lemma</term>
<term>Leuzinger</term>
<term>Level sets</term>
<term>Maximal</term>
<term>Minimal parabolic group</term>
<term>Next lemma</term>
<term>Noncompact</term>
<term>Noncompact type</term>
<term>Nonpositive curvature</term>
<term>Open neighbourhood</term>
<term>Parabolic</term>
<term>Quotient</term>
<term>Raghunathan</term>
<term>Reduction theory</term>
<term>Resp</term>
<term>Riemannian</term>
<term>Sect</term>
<term>Siegel</term>
<term>Subgroup</term>
<term>Sublevel</term>
<term>Sublevel sets</term>
<term>Submanifold</term>
<term>Subset</term>
<term>Symmetric</term>
<term>Symmetric quotient</term>
<term>Symmetric space</term>
<term>Symmetric spaces</term>
</keywords>
</textClass>
<langUsage><language ident="en">en</language>
</langUsage>
</profileDesc>
</teiHeader>
<front><div type="abstract" xml:lang="en">Abstract: LetX be a Riemannian symmetric space of noncompact type and rank≧2 and let Γ be a non-uniform, irreducible lattice. On the locally symmetric quotientV=Γ/X we construct an exhaustion functionh:V→[0,∞) whose sublevel sets {h≦s} are compact submanifolds ofV with corners. The top dimensional boundary faces of {h≦s} are parts of certain horospheres that join together at the corners. It can be shown that actually {h≦s} is a submanifold with corners isomorphic to the Borel-Serre compactification ofV.</div>
</front>
</TEI>
<affiliations><list><country><li>Suisse</li>
</country>
<region><li>Canton de Zurich</li>
</region>
<settlement><li>Zurich</li>
</settlement>
</list>
<tree><country name="Suisse"><region name="Canton de Zurich"><name sortKey="Leuzinger, Enrico" sort="Leuzinger, Enrico" uniqKey="Leuzinger E" first="Enrico" last="Leuzinger">Enrico Leuzinger</name>
</region>
<name sortKey="Leuzinger, Enrico" sort="Leuzinger, Enrico" uniqKey="Leuzinger E" first="Enrico" last="Leuzinger">Enrico Leuzinger</name>
</country>
</tree>
</affiliations>
</record>
Pour manipuler ce document sous Unix (Dilib)
EXPLOR_STEP=$WICRI_ROOT/Wicri/Mathematiques/explor/BourbakiV1/Data/Main/Exploration
HfdSelect -h $EXPLOR_STEP/biblio.hfd -nk 001C83 | SxmlIndent | more
Ou
HfdSelect -h $EXPLOR_AREA/Data/Main/Exploration/biblio.hfd -nk 001C83 | SxmlIndent | more
Pour mettre un lien sur cette page dans le réseau Wicri
{{Explor lien |wiki= Wicri/Mathematiques |area= BourbakiV1 |flux= Main |étape= Exploration |type= RBID |clé= ISTEX:33E2AF6547032913962C5A43884843D20BC7051E |texte= An exhaustion of locally symmetric spaces by compact submanifolds with corners }}
This area was generated with Dilib version V0.6.33. |