On the strict convexity of the K-energy

Berman, Robert,1976Gothenburg University,Göteborgs universitet,Institutionen för matematiska vetenskaper,Department of Mathematical Sciences,Chalmers tekniska högskola,Chalmers University of Technology,University of Gothenburg (author)

Let (X, L) be a polarized projective complex manifold. We show, by a simple toric one-dimensional example, that Mabuchi's K-energy functional on the geodesically complete space of bounded positive (1, 1)-forms in c(1)(L), endowed with the Mabuchi-Donaldson-Semmes metric, is not strictly convex modulo automorphisms. However, under some further assumptions the strict convexity in question does hold in the toric case. This leads to a uniqueness result saying that a finite energy minimizer of the K-energy (which exists on any toric polarized manifold (X, L) which is uniformly K-stable) is uniquely determined modulo automorphisms under the assumption that there exists some minimizer with strictly positive curvature current.

Göteborgs universitetInstitutionen för matematiska vetenskaper (creator_code:org_t)

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NATURAL SCIENCES: NATURAL SCIENCES; and Mathematics; and Discrete Mathema ...

NATURAL SCIENCES: NATURAL SCIENCES; and Mathematics; and Mathematical Ana ...

By the university: University of Gothenburg; Chalmers University of Technology

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