RELATIVE K-STABILITY AND MODIFIED K-ENERGY ON TORIC MANIFOLDS

By Bin Zhou, Xiaohua Zhu. 2006

82 citations recorded by the source corpus.

In this paper, we give a sufficient condition for both the relative K-stability and the properness of modified K-energy associated to Calabi's extremal metrics on toric manifolds. In addition, several examples of toric manifolds which satisfy the sufficient condition are presented.

Subfields: Applied Mathematics, Geometry and Topology, Health, Toxicology and Mutagenesis

View Paper: https://www.semanticscholar.org/paper/99f5c33bfde93264437f8fb98b251aa1792f7a4f

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

In Geometry and Topology

In Health, Toxicology and Mutagenesis

Citations in the corpus

Tian's properness conjectures and Finsler geometry of the space of Kahler metrics (2015, background): “To cite a few papers from a rapidly growing literature, we mention [16, 43, 52, 19, 53, 46, 69, 68] and references therein.”
Extremal metrics and K-stability (PhD thesis) (2006, background): “In [10] he showed that in the case of toric surfaces K-stability implies that the Mabuchi functional is bounded from below (this was later extended by Zhou-Zhu [38] to show properness of the Mabuchi functional) and a minimising sequence has a subsequence that converges in a weak sense.”
Extremal metrics and K‐stability (2004, background): “Since exp(vi) = 1, we find that fi(x) must be an integer.”
The Moser-Trudinger inequality on Kähler-Einstein manifolds (2006, background): “D inequality for Kähler-Einstein manifolds with positive first Chern class, when there are no holomorphic vector fields, and, more generally, when the setting is invariant under a maximal compact subgroup of the automorphism group.”
Extremal Kähler metrics on projective bundles over a curve (2009, methodology): “12Generalizing computations in [21, 66, 74], one can show that the value of F at a rational piecewise linear convex function computes the relative Futaki invariant introduced in [66] of a ‘compatible’ toric test configuration on (M,Ω); in general, one might need positivity of F on a larger space of ”
On the constant scalar curvature Kähler metrics, general automorphism group (2018, background): “(In the special case of toric varieties, Zhou-Zhu[41] proved the existence of toric invariant weak minimizers of the modified K-energy under properness assumption.”
Geodesic rays and stability in the cscK problem (2020, result): “This result was known by combining the works of Zhou-Zhu [72], Chen-Li-Sheng [22], Hisamoto [49] and Chen-Cheng [25, 26].”