Long time existence of Minimizing Movement solutions of Calabi flow

By Jeffrey Streets. 2012

49 citations recorded by the source corpus.

We recast the Calabi flow in DeGiorgi's language of minimizing movements. We establish the long time existence of minimizing movements for K-energy with arbitrary initial condition. Furthermore we establish some a priori regularity of these solutions, and that sufficiently regular minimizing movements are smooth solutions to Calabi flow.

Subfields: Applied Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/dd00032661e98bcc77680ce5b5da0257b133da0c

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

Citations in the corpus

On the constant scalar curvature Kähler metrics (II)—Existence results (2020, background): “Street[56], Berman-Darvas-Lu[6], the weak Calabi flow always exists globally.”
Kähler–Ricci flow, Kähler–Einstein metric, and K–stability (2015, background): “For instance, one can check the work of Chen-He [5],Tosatti-Weinkove [40], He [23], Streets [30], Huang-Feng [19], LiWang-Zheng [24] and the references therein for more information of the recent development.”
Tian's properness conjectures and Finsler geometry of the space of Kahler metrics (2015, unknown): “Other results include the work of Streets [54], who shows that one gains new insight on the long time behavior of the Calabi flow by placing it in the context of the abstract Riemannian metric completion of the Mabuchi metric.”
Smooth and singular Kahler-Einstein metrics (2014, background): “The most general long time existence result known is due to Streets [231] though the question of regularity of such weak flows is open (assuming curvature bounds along the flow a smooth solution exists for all time by Chen–He [64]).”