dc.contributor | Cardona Guio, Alexander | |
dc.contributor | Cortissoz Iriarte, Jean Carlos | |
dc.creator | Dorado Toro, Daniel Fernando | |
dc.date.accessioned | 2023-08-02T13:28:27Z | |
dc.date.accessioned | 2023-09-06T23:23:19Z | |
dc.date.available | 2023-08-02T13:28:27Z | |
dc.date.available | 2023-09-06T23:23:19Z | |
dc.date.created | 2023-08-02T13:28:27Z | |
dc.date.issued | 2023-06-01 | |
dc.identifier | http://hdl.handle.net/1992/69072 | |
dc.identifier | instname:Universidad de los Andes | |
dc.identifier | reponame:Repositorio Institucional Séneca | |
dc.identifier | repourl:https://repositorio.uniandes.edu.co/ | |
dc.identifier.uri | https://repositorioslatinoamericanos.uchile.cl/handle/2250/8726471 | |
dc.description.abstract | In this work, we use this moment map to relate solutions to certain differential equations to (i) diffeomorphisms of compact Riemann surfaces, (ii) additional Kähler metrics on a given compact Kähler manifold, and (iii) symplectic forms on 4-manifolds. | |
dc.language | eng | |
dc.publisher | Universidad de los Andes | |
dc.publisher | Matemáticas | |
dc.publisher | Facultad de Ciencias | |
dc.publisher | Departamento de Matemáticas | |
dc.relation | F. Klein, «Vergleichende Betrachtungen über neuere geometrische Forschungen», de, Mathematische Annalen 43, 63-100 (1893). | |
dc.relation | K. Mann, «The Structure of Homeomorphism and Diffeomorphism Groups», en, Notices of the Amer- ican Mathematical Society 68, 1 (2021). | |
dc.relation | S. K. Donaldson, «Moment maps and diffeomorphisms», Surveys in differential geometry 3, 107-127 (2002). | |
dc.relation | S. K. Donaldson, «Moment maps in differential geometry», Surveys in differential geometry 8, 171-189 (2003). | |
dc.relation | D. McDuff and D. Salamon, Introduction to symplectic topology (Oxford University Press, Mar. 2017). | |
dc.relation | R. H. Abraham and J. E. Marsden, Foundations of mechanics, eng, 2. ed., rev., enl., and reset (Perseus
Books, Cambridge, Mass, 2002). | |
dc.relation | R. Bryant, «An introduction to Lie groups and symplectic geometry», in Geometry and Quantum Field Theory, Vol. 1, edited by D. S. Freed and K. K. Uhlenbeck, IAS/Park City mathematics series (AMS and IAS/Park City Mathematics Institute, 1995), pp. 5-181. | |
dc.relation | D. Huybrechts, Complex geometry: an introduction, Universitext (Springer, Berlin ; New York, 2005), 309 pp. | |
dc.relation | N. Hitchin, «Hyperkähler manifolds», Séminaire Bourbaki 34, 137-166 (1992). | |
dc.relation | A. Schmeding, An introduction to infinite-dimensional differential geometry, Cambridge Studies in
Advanced Mathematics (Cambridge University Press, 2022). | |
dc.relation | H. Amiri, H. Glöckner, and A. Schmeding, «Lie groupoids of mappings taking values in a Lie groupoid», en, Archivum Mathematicum, 307-356 (2020). | |
dc.relation | A. Banyaga, The structure of classical diffeomorphism groups, Mathematics and Its Applications (Springer Verlag, 1997). | |
dc.relation | K.-H. Neeb, Infinite-Dimensional Lie Groups, 2005. | |
dc.relation | J. M. Lee, Introduction to smooth manifolds, 2nd ed, Graduate texts in mathematics 218 (Springer,
2013). | |
dc.relation | H. Hofer and E. Zehnder, Symplectic invariants and Hamiltonian dynamics, Birkhäuser Advanced Texts Basler Lehrbücher (Birkhäuser, Basel, 1994). | |
dc.relation | J. Marsden and A. Weinstein, «Reduction of symplectic manifolds with symmetry», en, Reports on Mathematical Physics 5, 121-130 (1974). | |
dc.relation | S. K. Donaldson and P. Kronheimer, The Geometry of Four-Manifolds, eng, Reprinted, Oxford math- ematical monographs (Clarendon Press, Oxford, 2007). | |
dc.relation | E. Calabi, «Métriques kählériennes et fibrés holomorphes», Annales scientifiques de l'École normale supérieure 12, 269-294 (1979). | |
dc.relation | P. Michor and C. Vizman, «n-transitivity of certain diffeomorphism groups.», Acta Mathematica Universitatis Comenianae. New Series 63, 221-225 (1994). | |
dc.relation | H. Omori, «On Banach-Lie groups acting on finite dimensional manifolds», Tohoku Mathematical Journal 30, 223-250 (1978). | |
dc.relation | J. B. Conway, A Course in Functional Analysis, en, Vol. 96, Graduate Texts in Mathematics (Springer New York, New York, NY, 2007). | |
dc.relation | R. Meise and D. Vogt, Introduction to functional analysis, Oxford graduate texts in mathematics 2 (Clarendon Press ; Oxford University Press, Oxford : New York, 1997). | |
dc.relation | P. W. Michor, Manifolds of differentiable mappings, Shiva mathematics series ; 3 (Shiva Pub, Orpington [Eng.], 1980). | |
dc.relation | L. C. Evans, Partial differential equations, 2nd ed, Graduate studies in mathematics v. 19, OCLC: ocn465190110 (American Mathematical Society, Providence, R.I, 2010). | |
dc.relation | C.-V. Pao, Nonlinear parabolic and elliptic equations, Softcover reprint of the hardcover 1st edition 1992 (Springer Science + Business Media, LLC, New York, 2013). | |
dc.relation | D. H. Phong, J. Song, and J. Sturm, «Complex Monge Ampere Equations», 10.48550/ARXIV.1209. 2203 (2012). | |
dc.relation | X. Chen, «On the lower bound of the Mabuchi energy and its application», International Mathematics Research Notices 2000, 607 (2000). | |
dc.rights | Attribution-NonCommercial-NoDerivatives 4.0 Internacional | |
dc.rights | http://creativecommons.org/licenses/by-nc-nd/4.0/ | |
dc.rights | info:eu-repo/semantics/openAccess | |
dc.rights | http://purl.org/coar/access_right/c_abf2 | |
dc.title | The moment map and the group of volume-preserving diffeomorphisms: applications to differential geometry | |
dc.type | Trabajo de grado - Pregrado | |