On the "Equation missing" Regularity of Geodesics in the Space of Kähler Metrics

Bedford, E., Taylor, B.A.: The Dirichlet problem for a complex Monge–Ampère equation. Invent. Math. 37(1), 1–44 (1976)

Berman, R.J.: On the optimal regularity of weak geodesics in the space of metrics on a polarized manifold. preprint arXiv:1405.6482

Berman, R.J., Berndtsson, B.: Convexity of the K-energy on the space of Kähler metrics and uniqueness of extremal metrics. J. Am. Math. Soc. 30(4), 1165–1196 (2017)

Błocki, Z.: On geodesics in the space of Kähler metrics. In: Advances in Geometric Analysis, Advanced Lectures in Mathematics (ALM), vol. 21, pp. 3–19. International Press, Somerville (2012)

Boucksom, S.: Monge–Ampère equations on complex manifolds with boundary. In: Complex Monge–Ampère equations and geodesics in the space of Kähler metrics, Lecture Notes in Mathematics, vol. 2038, pp. 257–282. Springer, Heidelberg (2012)

Caffarelli, L., Kohn, J.J., Nirenberg, L., Spruck, J.: The Dirichlet problem for nonlinear second-order elliptic equations. II. Complex Monge–Ampère, and uniformly elliptic, equations. Commun. Pure Appl. Math. 38(2), 209–252 (1985)

Chen, X.X.: The space of Kähler metrics. J. Differ. Geom. 56(2), 189–234 (2000)

Chen, X.X., Li, L., Păun, M.: Approximation of weak geodesics and subharmonicity of Mabuchi energy. Ann. Fac. Sci. Toulouse Math. (6) 25(5), 935–957 (2016)

Chen, X.X., Tian, G.: Geometry of Kähler metrics and foliations by holomorphic discs. Publ. Math. Inst. Hautes Études Sci. 107, 1–107 (2008)

Chu, J., Tosatti, V., Weinkove, B.: The Monge–Ampère equation for non-integrable almost complex structures. J. Eur. Math. Soc. (to appear)

Chu, J., Tosatti, V., Weinkove, B.: $$C^{1,1}$$ regularity for degenerate complex Monge–Ampère equations and geodesic rays. preprint arXiv: 1707.03660

Darvas, T.: Morse theory and geodesics in the space of Kähler metrics. Proc. Am. Math. Soc. 142(8), 2775–2782 (2014)

Darvas, T., Lempert, L.: Weak geodesics in the space of Kähler metrics. Math. Res. Lett. 19(5), 1127–1135 (2012)

Donaldson, S.K.: Symmetric spaces, Kähler geometry and Hamiltonian dynamics. In: Northern California Symplectic Geometry Seminar, pp. 13–33. American Mathematical Society, Providence, RI (1999)

Donaldson, S.K.: Holomorphic discs and the complex Monge–Ampère equation. J. Symplectic Geom. 1(2), 171–196 (2002)

Guan, B.: The Dirichlet problem for complex Monge–Ampère equations and regularity of the pluri-complex Green function. Commun. Anal. Geom. 6(4), 687–703 (1998)

Guan, B., Li, Q.: Complex Monge–Ampère equations and totally real submanifolds. Adv. Math. 225(3), 1185–1223 (2010)

He, W.: On the space of Kähler potentials. Commun. Pure Appl. Math. 68(2), 332–343 (2015)

Lempert, L., Vivas, L.: Geodesics in the space of Kähler metrics. Duke Math. J. 162(7), 1369–1381 (2013)

Mabuchi, T.: Some symplectic geometry on compact Kähler manifolds. I. Osaka J. Math. 24(2), 227–252 (1987)

Phong, D.H., Song, J., Sturm, J.: Complex Monge-Ampère equations. In: Cao, H.-D., Yau, S.-T. (eds.) Surveys in Differential Geometry, vol. 17, pp. 327–411. International Press, Boston, MA (2012)

Phong, D.H., Sturm, J.: The Monge–Ampère operator and geodesics in the space of Kähler potentials. Invent. Math. 166(1), 125–149 (2006)

Phong, D.H., Sturm, J.: Test configurations for K-stability and geodesic rays. J. Symplectic Geom. 5(2), 221–247 (2007)

Phong, D.H., Sturm, J.: The Dirichlet problem for degenerate complex Monge–Ampère equations. Commun. Anal. Geom. 18(1), 145–170 (2010)

Phong, D.H., Sturm, J.: Regularity of geodesic rays and Monge–Ampère equations. Proc. Am. Math. Soc. 138(10), 3637–3650 (2010)

Pliś, S.: The Monge–Ampère equation on almost complex manifolds. Math. Z. 276, 969–983 (2014)

Ross, J., Witt Nyström, D.: Harmonic discs of solutions to the complex homogeneous Monge–Ampère equation. Publ. Math. Inst. Hautes Études Sci. 122, 315–335 (2015)

Ross, J., Witt Nyström, D.: On the maximal rank problem for the complex homogeneous Monge–Ampère equation. preprint arXiv:1610.02280

Semmes, S.: Complex Monge–Ampère and symplectic manifolds. Am. J. Math. 114(3), 495–550 (1992)

Székelyhidi, G.: Fully non-linear elliptic equations on compact Hermitian manifolds. J. Differ. Geom. (to appear)

Székelyhidi, G., Tosatti, V., Weinkove, B.: Gauduchon metrics with prescribed volume form. preprint arxiv:1503.04491

Tosatti, V., Weinkove, B.: The complex Monge–Ampère equation on compact Hermitian manifolds. J. Am. Math. Soc. 23(4), 1187–1195 (2010)

Yau, S.-T.: On the Ricci curvature of a compact Kähler manifold and the complex Monge–Ampère equation, I. Commun. Pure Appl. Math. 31(3), 339–411 (1978)