Minimizing weak solutions for calabi�s extremal metrics on toric manifolds

Bin Zhou; Xiaohua Zhu
June 2008
Calculus of Variations & Partial Differential Equations;Jun2008, Vol. 32 Issue 2, p191
Academic Journal
In this paper, we discuss Donaldson�s version of the modified K-energy associated to the Calabi�s extremal metrics on toric manifolds and prove the existence of the weak solution for extremal metrics in the sense of convex functions which minimizes the modified K-energy.


Related Articles

  • KAM THEORY: THE LEGACY OF KOLMOGOROV'S 1954 PAPER. Broer, Henk W. // Bulletin (New Series) of the American Mathematical Society;Oct2004, Vol. 41 Issue 4, p507 

    Kolmogorov-Arnold-Moser (or KAM) theory was developed for conservative dynamical systems that are nearly integrable. Integrable systems in their phase space usually contain lots of invariant tori, and KAM theory establishes persistence results for such tori, which carry quasi-periodic motions....

  • Hilbert Polynomial of the Kimura 3-Parameter Model. Kubjas, Kaie // Journal of Algebraic Statistics;Jan2012, Vol. 3 Issue 1, p64 

    In [2] Buczyńska and Wiśniewski showed that the Hilbert polynomial of the algebraic variety associated to the Jukes-Cantor binary model on a trivalent tree depends only on the number of leaves of the tree and not on its shape. We ask if this can be generalized to other group-based...

  • On the extension of Calabi flow on toric varieties. Huang, Hongnian // Annals of Global Analysis & Geometry;Jun2011, Vol. 40 Issue 1, p1 

    Inspired by recent study of Donaldson on constant scalar curvature metrics on toric complex surfaces, we study obstructions to the extension of the Calabi flow on a polarized toric variety. Under some technical assumptions, we prove that the Calabi flow can be extended for all time.

  • Localization and Gluing of Topological Amplitudes. Diaconescu, Duiliu-Emanuel; Florea, Bogdan // Communications in Mathematical Physics;Jul2005, Vol. 257 Issue 1, p119 

    We develop a gluing algorithm for Gromov-Witten invariants of toric Calabi-Yau threefolds based on localization and gluing graphs. The main building block of this algorithm is a generating function of cubic Hodge integrals of special form. We conjecture a precise relation between this generating...

  • Chow rings of toric varieties defined by atomic lattices. Feichtner, Eva Maria; Yuzvinsky, Sergey // Inventiones Mathematicae;Mar2004, Vol. 155 Issue 3, p515 

    We study a graded algebra D = D(L, G) over Z defined by a finite lattice L and a subset G in L, a so-called building set. This algebra is a generalization of the cohomology algebras of hyperplane arrangement compactifications found in work of De Concini and Procesi. Our main result is a...

  • Convex Polytopes and Quasilattices from the Symplectic Viewpoint. Battaglia, Fiammetta // Communications in Mathematical Physics;Jan2007, Vol. 269 Issue 2, p283 

    We construct, for each convex polytope, possibly nonrational and nonsimple, a family of compact spaces that are stratified by quasifolds, i.e. each of these spaces is a collection of quasifolds glued together in an suitable way. A quasifold is a space locally modelled on $${\mathbb{R}^{k}}$$...

  • Fiber Fans and Toric Quotients. Alastair Craw; Diane Maclagan // Discrete & Computational Geometry;Feb2007, Vol. 37 Issue 2, p251 

    Abstract??The GIT chamber decomposition arising from a subtorus action on a polarized quasiprojective toric variety is a polyhedral complex. Denote by ? the fan that is the cone over the polyhedral complex. In this paper we show that the toric variety defined by the fan ? is the normalization of...

  • Solvable Systems of Equations Modeled on Some Spines of 3-Manifolds. Kopteva, N. V. // Siberian Mathematical Journal;Mar/Apr2003, Vol. 44 Issue 2, p278 

    We show solvability of the systems of equations modeled on certain spines of 3-manifolds. We extend a result by Duncan and Howie about the 2-skeleton of the 3-torus.

  • Classification of Toric 2-Fano 4-folds. Nobili, Edilaine // Bulletin of the Brazilian Mathematical Society;Sep2011, Vol. 42 Issue 3, p399 

    In this notes we classify toric Fano 4-folds having positive second Chern character.


Read the Article


Sorry, but this item is not currently available from your library.

Try another library?
Sign out of this library

Other Topics