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Abstract:

We study the multiplicity of positive solutions of a Brezis-Nirenberg-type problem on a region of the three-dimensional sphere, which is invariant by the natural torus action. In the paper by Brezis and Peletier, the case in which the region is invariant by the SO(3)-action is considered, namely, when the region is a spherical cap. We prove that the number of positive solutions increases as the parameter of the equation tends to -∞, giving an answer to a particular case of an open problem proposed in the above referred paper. © 2019 World Scientific Publishing Company.

Registro:

Documento: Artículo
Título:Elliptic equations with critical exponent on a torus invariant region of 3
Autor:Rey, C.A.
Filiación:Departamento de Matemática, Universidad de Buenos Aires Ciudad Universitaria, Pabellón I, Buenos Aires, C1428EGA, Argentina
Palabras clave:Brezis-Nirenberg problem; Nonlinear elliptic equations; Yamabe equation
Año:2019
Volumen:21
Número:2
DOI: http://dx.doi.org/10.1142/S0219199717501000
Título revista:Communications in Contemporary Mathematics
Título revista abreviado:Commun. Contemp. Math.
ISSN:02191997
Registro:http://digital.bl.fcen.uba.ar/collection/paper/document/paper_02191997_v21_n2_p_Rey

Referencias:

  • Alexakis, S., Mazzeo, R., Renormalized area and properly embedded minimal surfaces in hyperbolic 3-manifolds (2010) Comm. Math. Phys., 297 (3), pp. 621-651. , arXiv:0802.2250
  • Anderson, M., L2 curvature and volume renormalization of the ahe metrics on 4-manifolds (2001) Math. Res. Lett., 8, pp. 171-188. , arXiv:math/0011051
  • Andersson, L., Chrúsciel, P.T., Friedrich, H., On the regularity of solutions to the yamabe equation and the existence of smooth hyperboloidal initial data for Einstein's field equations (1992) Comm. Math. Phys., 149 (3), pp. 587-612. , arXiv:0802.2250
  • Astaneh, A.F., Berthiere, C., Fursaev, D., Solodukhin, S.N., (2017) Holographic Calculation of Entanglement Entropy In The Presence of Boundaries, , preprint. arXiv: 1703.04186
  • Baum, H., Juhlrfaut, A., (2010) Conformal Differential Geometry: Q-Curvature and Conformal Holonomy, , Birkhäuser
  • Ben-Ami, O., Carmi, D., On Volumes of Subregions In Holography And Complexity, , arXiv:1609.02514
  • Branson, T.P., Sharp inequalities, the functional determinant, and the complementary series (1995) Trans. Amer. Math. Soc., 347 (10), pp. 3671-3742
  • Branson, T.P., Orsted, B., Explicit functional determinants in four dimensions (1991) Proc. Amer. Math. Soc., 113, pp. 669-682
  • Brown, A.R., Roberts, D.A., Susskind, L., Swingle, B., Zhao, Y., Holographic complexity equals bulk action? (2016) Phys. Rev. Lett., 116, p. 191301. , arXiv:1509.07876
  • Chang, S.Y.A., Qing, J., The zeta functional determinants on manifolds with boundary. I. The formula (1997) J. Funct. Anal., 147, pp. 327-362
  • Chang, S.Y.A., Qing, J.J., Yang, P., On the renormalized volumes for conformally compact Einstein manifolds (2008) J. Math. Sci. (NY)., 149, pp. 1755-1769. , arXiv:math/0512376
  • Cherrier, P., Problèmes de Neumann non linéaires sur les variétés riemanniennes (1984) J. Funct. Anal., 57 (2), pp. 154-206
  • Fefferman, C., Graham, C.R., Q-curvature and poincaré metrics (2002) Math. Res. Lett., 9 (2-3), pp. 139-151. , arXiv:math/0110271
  • Fischetti, S., Wiseman, T., (2016) A Bound On Holographic Entanglement Entropy From Inverse Mean Curvature Flow, , preprint. arXiv:1612.04373
  • Glaros, M., Gover, A.R., Halbasch, M., Waldron, A., (2015) Singular Yamabe Problem Willmore Energies, , preprint. arXiv:1508.01838
  • Gover, A.R., Conformal dirichlet-neumann maps and poincaré-Einstein manifolds (2007) Symmetry Integrab. Geom. Methods Appl., 3, pp. 100-121. , arXiv:0710.2585
  • Gover, A.R., Einstein, A., And poincaré-Einstein manifolds in riemannian signature (2010) J. Geom. Phys., 60 (2), pp. 182-204. , arXiv:0803.3510
  • Gover, A.R., Peterson, L., (2018) Conformal Boundary Operators, T-Curvatures, And Conformal Fractional Laplacians of Odd Order, , preprint. arXiv:1802.08366
  • Gover, A.R., Waldron, A., Boundary calculus for conformally compact manifolds (2014) Indiana Univ. Math. J., 63 (1), pp. 119-163. , arXiv: 1104.2991
  • Gover, A.R., Waldron, A., Submanifold conformal invariants and a boundary yamabe problem (2015) Extended Abstracts Fall 2013, Trends in Mathematics, pp. 21-26. , Birkhäuser
  • Gover, A.R., Waldron, A., (2015) Conformal Hypersurface Geometry Via A Boundary Loewner-Nirenberg-Yamabe Problem, , preprint. arXiv:1506.02723
  • Gover, A.R., Waldron, A., Renormalized volume (2017) Comm. Math. Phys., 354 (3), pp. 1205-1244. , arXiv: 1603.07367
  • Gover, A.R., Waldron, A., (2016) A Calculus For Conformal Hypersurfaces And New Higher Willmore Energy Functionals, , preprint. arXiv:1611.04055
  • Graham, C.R., Volume and area renormalizations for conformally compact Einstein metrics (2000) Rend. Circ. Mat. Palermo, 2, pp. 31-42. , arXiv:math/9909042
  • Graham, C.R., (2016) Volume Renormalization For Singular Yamabe Metrics, , preprint; arXiv: 1606.00069
  • Graham, C.R., Witten, E., Conformal anomaly of submanifold observables in ads/cft correspondence (1999) Nuclear Phys. B, 546 (1-2), pp. 52-64. , arXiv:hep-Th/9901021
  • Gubser, S.S., Klebanov, I.R., Polyakov, A.M., Gauge theory correlators from non-critical string theory (1998) Phys. Lett. B, 428, pp. 105-114. , arXiv:hep-Th/9802109
  • Henningson, M., Skenderis, K., The holographic weyl anomaly (1998) J. High Energy Phys., 1998, p. 12p. , Paper No. 23.; arXiv:hep-Th/hep-Th9806087
  • Maldacena, J., The large n limit of superconformal field theories and supergravity (1998) Adv. Theor. Math. Phys., 2, pp. 231-252. , arXiv:hep-Th/9711200
  • Ndiaye, C.B., Conformal metrics with constant q-curvature for manifolds with boundary (2008) Comm. Anal. Geom., 16, pp. 1049-1124
  • Ndiaye, C.B., Constant t-curvature conformal metrics on 4-manifolds with boundary (2009) Pacific J. Math., 240, pp. 151-184. , arXiv:0708.0732
  • Ndiaye, C.B., Q-curvature flow on 4-manifolds with boundary (2011) Math. Z., 269, pp. 83-114. , arXiv:0708.2029
  • Seshadri, N., Volume renormalization for complete Einstein-kähler metrics (2007) Differential Geom. Appl., 25, pp. 356-379. , arXiv:math/0404455
  • Solodukhin, S.N., (2015) Boundary Terms of Conformal Anomaly, , preprint;arXiv: 1510.04566
  • Stafford, R., (2005) Tractor Calculus And Invariants For Conformal Sub-Manifolds, , Master's thesis, University of Auckland
  • Vyatkin, Y., (2013) Manufacturing Conformal Invariants of Hypersurfaces, , Ph.D. thesis, University of Auckland
  • Witten, E., Anti de sitter space and holography (1998) Adv. Theor. Math. Phys., 2, pp. 253-291. , arXiv:hep-Th/9802150

Citas:

---------- APA ----------
(2019) . Elliptic equations with critical exponent on a torus invariant region of 3. Communications in Contemporary Mathematics, 21(2).
http://dx.doi.org/10.1142/S0219199717501000
---------- CHICAGO ----------
Rey, C.A. "Elliptic equations with critical exponent on a torus invariant region of 3" . Communications in Contemporary Mathematics 21, no. 2 (2019).
http://dx.doi.org/10.1142/S0219199717501000
---------- MLA ----------
Rey, C.A. "Elliptic equations with critical exponent on a torus invariant region of 3" . Communications in Contemporary Mathematics, vol. 21, no. 2, 2019.
http://dx.doi.org/10.1142/S0219199717501000
---------- VANCOUVER ----------
Rey, C.A. Elliptic equations with critical exponent on a torus invariant region of 3. Commun. Contemp. Math. 2019;21(2).
http://dx.doi.org/10.1142/S0219199717501000