Interior estimates for the n-dimensional Abreu's equation

• Autores: Bohui Chen, Qing Han, An-Min Li, Li Sheng
• Localización: Advances in mathematics, ISSN 0001-8708, Vol. 251, Nº 1, 2014, págs. 35-46
• Idioma: inglés
• DOI: 10.1016/j.aim.2013.10.004
• Texto completo no disponible (Saber más ...)
• Referencias bibliográficas
  • M. Abreu, Kähler geometry of toric varieties and extremal metrics, Internat. J. Math. 9 (1998) 641–651.
  • L.A. Caffarelli, Interior W2,p estimates for solutions of Monge–Ampère equations, Ann. Math. 131 (1990) 135–150.
  • L.A. Caffarelli, C.E. Gutiérrez, Properties of the solutions of the linearized Monge–Ampère equations, Amer. J. Math. 119 (1997) 423–465.
  • X. Chen, S.K. Donaldson, S. Sun, Kähler–Einstein metrics on Fano manifolds, I, arXiv:1211.4566; X. Chen, S.K. Donaldson, S. Sun, Kähler–Einstein...
  • B. Chen, A.-M. Li, L. Sheng, The Abreu equation with degenerated boundary conditions, J. Differential Equations 252 (2012) 5235–5259.
  • B. Chen, A.-M. Li, L. Sheng, Interior regularity on the Abreu equation, Acta Math. Sinica 29 (2013) 33–38.
  • B. Chen, A.-M. Li, L. Sheng, Affine techniques on extremal metrics on toric surfaces, arXiv:1008.2606.
  • B. Chen, A.-M. Li, L. Sheng, Extremal metrics on toric surfaces, arXiv:1008.2607.
  • B. Chen, A.-M. Li, L. Sheng, Uniform K-stability for extremal metrics on toric varieties, arXiv:1109.5228v2.
  • S.K. Donaldson, Scalar curvature and stability of toric varieties, J. Differential Geom. 62 (2002) 289–349.
  • S.K. Donaldson, Interior estimates for solutions of Abreu’s equation, Collect. Math. 56 (2005) 103–142.
  • S.K. Donaldson, Extremal metrics on toric surfaces: a continuity method, J. Differential Geom. 79 (2008) 389–432.
  • S.K. Donaldson, Constant scalar curvature metrics on toric surfaces, Geom. Funct. Anal. 19 (2009) 83–136.
  • R. Feng, G. Székelyhidi, Periodic solutions of Abreu’s equation, Math. Res. Lett. 18 (2011) 1271–1279.
  • V. Guillemin, Kähler structures on toric varieties, J. Differential Geom. 40 (1994) 285–309.
  • A.-M. Li, F. Jia, A Bernstein properties of some fourth order partial differential equations, Results Math. 56 (2009) 109–139.
  • A.-M. Li, R. Xu, U. Simon, F. Jia, Affine Bernstein Problems and Monge–Ampère Equations, World Scientific, 2010.
  • G. Sziékelyhidi, Extremal metrics and K-stability, Bull. Lond. Math. Soc. 39 (2007) 76–84.
  • G. Tian, Kähler–Einstein metrics with positive scalar curvature, Invent. Math. 130 (1997) 1–39.
  • G. Tian, Canonical Metrics in Kähler Geometry, Lectures Math. ETH Zurich, Birkhäuser Verlag, Basel, 2000.
  • G. Tian, Extremal metrics and geometric stability, Houston J. Math. 28 (2002) 411–432.
  • G. Tian, K-stability and Kähler–Einstein metrics, arXiv:1211.4669.
  • N.S. Trudinger, X. Wang, Berstein–Jörgens theorem for a fourth order partial differential equation, J. Partial Differ. Equ. 15 (2002) 78–88.
  • S.-T. Yau, Open problems in geometry, in: Proc. Sympos. Pure Math., vol. 54, 1993, pp. 1–28.