Tokyo Journal of Mathematics

On the $C^\alpha$-convergence of the Solution of the Chern-Ricci Flow on Elliptic Surfaces

Masaya KAWAMURA

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Abstract

We will study the Chern-Ricci flow on non-Kähler properly elliptic surfaces. These surfaces are compact complex surfaces whose first Betti number is odd, Kodaira dimension is equal to 1 and admit an elliptic fibration to a smooth compact curve. We will show that a solution of the Chern-Ricci flow converges in $C^\alpha$-topology on these elliptic surfaces by choosing a special initial metric.

Article information

Source
Tokyo J. Math., Volume 39, Number 1 (2016), 215-224.

Dates
First available in Project Euclid: 30 March 2016

Permanent link to this document
https://projecteuclid.org/euclid.tjm/1459367266

Digital Object Identifier
doi:10.3836/tjm/1459367266

Mathematical Reviews number (MathSciNet)
MR3543140

Zentralblatt MATH identifier
1357.53079

Subjects
Primary: 53C44: Geometric evolution equations (mean curvature flow, Ricci flow, etc.)
Secondary: 53C55: Hermitian and Kählerian manifolds [See also 32Cxx] 32W20: Complex Monge-Ampère operators

Citation

KAWAMURA, Masaya. On the $C^\alpha$-convergence of the Solution of the Chern-Ricci Flow on Elliptic Surfaces. Tokyo J. Math. 39 (2016), no. 1, 215--224. doi:10.3836/tjm/1459367266. https://projecteuclid.org/euclid.tjm/1459367266


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