Convergence rate of the weighted conformal mean curvature flow
In this article, we study the convergence rate of the following Yamabe-type flow Rϕ(t)m=0inMand∂∂tg(t)=2(hϕ(t)m−Hϕ(t)m)g(t)∂∂tϕ(t)=m(Hϕ(t)m−hϕ(t)m)on∂M{R}_{\phi \left(t)}^{m}=0\hspace{0.33em}\hspace{0.1em}\text{in}\hspace{0.1em}\hspace{0.33em}M\hspace{1em}\hspace{0.1em}\text{and}\hspace{0.1em}\hspac...
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
De Gruyter
2025-07-01
|
| Series: | Analysis and Geometry in Metric Spaces |
| Subjects: | |
| Online Access: | https://doi.org/10.1515/agms-2025-0026 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Summary: | In this article, we study the convergence rate of the following Yamabe-type flow Rϕ(t)m=0inMand∂∂tg(t)=2(hϕ(t)m−Hϕ(t)m)g(t)∂∂tϕ(t)=m(Hϕ(t)m−hϕ(t)m)on∂M{R}_{\phi \left(t)}^{m}=0\hspace{0.33em}\hspace{0.1em}\text{in}\hspace{0.1em}\hspace{0.33em}M\hspace{1em}\hspace{0.1em}\text{and}\hspace{0.1em}\hspace{1em}\left\{\begin{array}{l}\frac{\partial }{\partial t}g\left(t)=2\left({h}_{\phi \left(t)}^{m}-{H}_{\phi \left(t)}^{m})g\left(t)\\ \frac{\partial }{\partial t}\phi \left(t)=m\left({H}_{\phi \left(t)}^{m}-{h}_{\phi \left(t)}^{m})\end{array}\right.\hspace{0.33em}\hspace{0.1em}\text{on}\hspace{0.1em}\hspace{0.33em}\partial M on a smooth metric measure space with boundary (M,g(t),e−ϕ(t)dVg(t),e−ϕ(t)dAg(t),m)\left(M,g\left(t),{e}^{-\phi \left(t)}{\rm{d}}{V}_{g\left(t)},{e}^{-\phi \left(t)}{\rm{d}}{A}_{g\left(t)},m), where Rϕ(t)m{R}_{\phi \left(t)}^{m} is the weighted scalar curvature, Hϕ(t)m{H}_{\phi \left(t)}^{m} is the weighted mean curvature, and hϕ(t)m{h}_{\phi \left(t)}^{m} is the average of the weighted mean curvature. |
|---|---|
| ISSN: | 2299-3274 |