The paper extends the Sobolev-type inequalities of Guo-Phong-Song-Sturm and Guedj-Tô from functions to twisted differential forms using heat kernel estimates.
Diameter estimates in K\"ahler geometry
1 Pith paper cite this work. Polarity classification is still indexing.
1
Pith paper citing it
abstract
Diameter estimates for K\"ahler metrics are established which require only an entropy bound and no lower bound on the Ricci curvature. The proof builds on recent PDE techniques for $L^\infty$ estimates for the Monge-Amp\`ere equation, with a key improvement allowing degeneracies of the volume form of codimension strictly greater than one. As a consequence, diameter bounds are obtained for long-time solutions of the K\"ahler-Ricci flow and finite-time solutions when the limiting class is big, as well as for special fibrations of Calabi-Yau manifolds.
fields
math.CV 1years
2025 1verdicts
CONDITIONAL 1representative citing papers
citing papers explorer
-
Estimates of heat kernels and Sobolev-type inequalities for twisted differential forms on compact K\"ahler manifolds
The paper extends the Sobolev-type inequalities of Guo-Phong-Song-Sturm and Guedj-Tô from functions to twisted differential forms using heat kernel estimates.