Convergence of the $J$-flow on toric manifolds
By Tristan C. Collins, G'abor Sz'ekelyhidi. 2014
91 citations recorded by the source corpus.
We show that on a Kahler manifold whether the J-flow converges or not is independent of the chosen background metric in its Kahler class. On toric manifolds we give a numerical characterization of when the J-flow converges, verifying a conjecture of Lejmi and the second author in this case. We also strengthen existing results on more general inverse $\sigma_{k}$ equations on Kahler manifolds.
Subfields: Applied Mathematics, Geometry and Topology
View Paper: https://www.semanticscholar.org/paper/70c8eb9bfe6b1957ae103863dbdbbd20d5926c5a
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In Applied Mathematics
In Geometry and Topology
Citations in the corpus
- Geodesic rays and stability in the cscK problem (2020, background): “It is a result by Song-Weinkove [64] that if the two conditions are satisfied, the corresponding J-equation is solvable, and by [28] the Archimedean JKX+ L-energy is proper, which implies the last statement.”
- Gauduchon metrics with prescribed volume form (2015, unknown): “Some other works on this topic include [6], [7], [14]–[17], [23]–[25], [27], [28], [32], [33], [41], [42], [44]–[46].”
- A class of curvature type equations. (2019, unknown): “Moreover, equations of the form σ1(D u) + b σn(D u) = C for some constants b ≥ 0 and C > 0 also arise from the study of J-equation on toric varieties by Collins-Székelyhidi [10].”
- On the constant scalar curvature Kähler metrics, general automorphism group (2018, unknown): “To see that Jω0 is proper, this follows from Proposition 22 in [22], which says that for some δ > 0 and some C > 0, one has Jω0(φ) ≥ δJ(φ) − C, for any φ ∈ H0.”
- Nakai-Moishezon criterions for complex Hessian equations (2020, background): “Both the J-equation and the J-flow are extensively studied in [3, 4, 22, 23, 19, 13, 20, 16, 7, 21, 12, 6].”