| Title:
|
Some evolution equations under the List's flow and their applications (English) |
| Author:
|
Ma, Bingqing |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
55 |
| Issue:
|
1 |
| Year:
|
2014 |
| Pages:
|
41-52 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
In this paper, we consider some
evolution equations of generalized
Ricci curvature and generalized scalar
curvature under the List's flow.
As applications, we obtain $L^2$-estimates
for generalized scalar curvature and
the first variational formulae for
non-negative eigenvalues with respect
to the Laplacian. (English) |
| Keyword:
|
List's flow |
| Keyword:
|
eigenvalue |
| Keyword:
|
scalar curvature |
| MSC:
|
53C21 |
| MSC:
|
53C44 |
| idZBL:
|
Zbl 06383784 |
| idMR:
|
MR3160825 |
| . |
| Date available:
|
2014-01-17T09:33:35Z |
| Last updated:
|
2016-04-04 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/143567 |
| . |
| Reference:
|
[1] Cao X.D., Hamilton R.: Differential Harnack estimates for time-dependent heat equations with potentials.Geom. Funct. Anal. 19 (2009), 989–1000. Zbl 1183.53059, MR 2570311, 10.1007/s00039-009-0024-4 |
| Reference:
|
[2] Fang S.W.: Differential Harnack inequalities for heat equations with potentials under the Bernhard List's flow.Geom. Dedicata 161 (2012), 11–22. Zbl 1253.53034, MR 2994028, 10.1007/s10711-011-9690-0 |
| Reference:
|
[3] Ma B.Q., Huang G.Y.: Lower bounds for the scalar curvature of noncompact gradient solitons of List's flow.Arch. Math. 100 (2013), 593–599. MR 3069112, 10.1007/s00013-013-0534-z |
| Reference:
|
[4] Li Y.: Eigenvalues and entropys under the harmonic-Ricci flow.arXiv:1011.1697, to appear in Pacific J. Math. |
| Reference:
|
[5] List B.: Evolution of an extended Ricci flow system.PhD Thesis, AEI Potsdam, http://www.diss.fu-berlin.de/2006/180/index.html (2006). Zbl 1166.53044 |
| Reference:
|
[6] List B.: Evolution of an extended Ricci flow system.Comm. Anal. Geom. 16 (2008), 1007–1048. Zbl 1166.53044, MR 2471366, 10.4310/CAG.2008.v16.n5.a5 |
| Reference:
|
[7] Lott J., Sesum N.: Ricci flow on three-dimensional manifolds with symmetry.arXiv:1102.4384, to appear in Comm. Math. Helv. |
| Reference:
|
[8] Müller R.: Ricci flow coupled with harmonic map flow.Ann. Sci. Éc. Norm. Supér. 45 (2012), 101–142. Zbl 1247.53082, MR 2961788 |
| Reference:
|
[9] Qian Z.M.: Ricci flow on a $3$-manifold with positive scalar curvature.Bull. Sci. Math. 133 (2009), 145–168. Zbl 1160.53368, MR 2494463, 10.1016/j.bulsci.2007.12.002 |
| Reference:
|
[10] Wang L.F.: Differential Harnack inequalities under a coupled Ricci flow.Math. Phys. Anal. Geom. 15 (2012), 343–360. Zbl 1257.53101, MR 2996456, 10.1007/s11040-012-9115-9 |
| . |
