Conic manifolds under the Yamabe flow

Roidos, Nikolaos

doi:10.1007/s00028-019-00521-9

Search citation statements

Order By: Relevance

Paper Sections

Select...

Citation Types

Supporting

Mentioning

Contrasting

Year Published

2021

2023

Publication Types

Select...

Article2

Other1

Relationship

Self Cite0

Independent3

Authors

Journals

Cited by 3 publications

(2 citation statements)

References 22 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…On incomplete surfaces, where Ricci and Yamabe flows coincide, Giesen and Topping [GiTo10,GiTo11] constructed a flow that becomes instantaneously complete. In higher dimensions, we have the work of Roidos [Roi20], which establishes existence of the Yamabe-flow in the presence of a cone singularity as long as the initial scalar curvature is in L q (M) for some q > n 2 . See the short discussion in Subsection 1.3 below for the geometric interpretation.…”

mentioning

confidence: 99%

See 1 more Smart Citation

Convergence of the Yamabe flow on singular spaces with positive Yamabe constant

Carron¹,

Olsen²,

Vertman³

2021

Preprint

View full text Add to dashboard Cite

In this work, we study the convergence of the normalized Yamabe flow with positive Yamabe constant on a class of pseudo-manifolds that includes stratified spaces with iterated cone-edge metrics. We establish convergence under a low-energy condition. We also prove a concentration-compactness dichotomy, and investigate what the alternatives to convergence are. We end by investigating a non-convergent example due to Viaclovsky in more detail.

show abstract

mentioning

confidence: 99%

“…See the short discussion in Subsection 1.3 below for the geometric interpretation. Convergence is not discussed in [Roi20].…”

mentioning

confidence: 99%