scholarly journals Correction to: Stability of ALE Ricci-Flat Manifolds Under Ricci Flow

2021 ◽  
Author(s):  
Alix Deruelle ◽  
Klaus Kröncke
Keyword(s):  
Ricci Flow ◽  
Ricci Flat ◽  
Flat Manifolds

scholarly journals A C0-estimate for the parabolic Monge–Ampère equation on complete non-compact Kähler manifolds

2009 ◽  
Vol 146 (1) ◽  
pp. 259-270 ◽  
Author(s):  
Albert Chau ◽  
Luen-Fai Tam
Keyword(s):  
Ricci Flow ◽  
Kähler Manifolds ◽  
Main Step ◽  
Kahler Manifolds ◽  
Compact Sets ◽  
Ricci Flat ◽  
Long Time ◽  
Flat Manifolds ◽  
Monge Ampere ◽  
Invent Math

AbstractIn this article we study the Kähler–Ricci flow, the corresponding parabolic Monge–Ampère equation and complete non-compact Kähler–Ricci flat manifolds. Our main result states that if (M,g) is sufficiently close to being Kähler–Ricci flat in a suitable sense, then the Kähler–Ricci flow has a long time smooth solution g(t) converging smoothly uniformly on compact sets to a complete Kähler–Ricci flat metric on M. The main step is to obtain a uniform C0-estimate for the corresponding parabolic Monge–Ampère equation. Our results on this can be viewed as parabolic versions of the main results of Tian and Yau [Complete Kähler manifolds with zero Ricci curvature. II, Invent. Math. 106 (1990), 27–60] on the elliptic Monge–Ampère equation.

scholarly journals MORE M-BRANES ON PRODUCT OF RICCI-FLAT MANIFOLDS

2012 ◽  
Vol 09 (08) ◽  
pp. 1250067 ◽  
Author(s):  
V. D. IVASHCHUK
Keyword(s):  
Ricci Flat ◽  
Flat Manifolds ◽  
Fractional Numbers

Partially supersymmetric intersecting (non-marginal) composite M-brane solutions defined on the product of Ricci-flat manifolds M0 × M1 × ⋯ × Mn in D = 11 supergravity are considered and formulae for fractional numbers of unbroken supersymmetries are derived for the following configurations of branes: M2 ∩ M2, M2 ∩ M5, M5 ∩ M5 and M2 ∩ M2 ∩ M2. Certain examples of partially supersymmetric configurations are presented.

scholarly journals The Kähler-Ricci flow, Ricci-flat metrics and collapsing limits

2018 ◽  
Vol 140 (3) ◽  
pp. 653-698 ◽  
Author(s):  
Valentino Tosatti ◽  
Ben Weinkove ◽  
Xiaokui Yang
Keyword(s):  
Ricci Flow ◽  
Ricci Flat
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