PDF
Abstract
The authors prove a rigidity result of Lagrangian translating solitons in ℝ2n, which extends the result of [Han, X. and Sun, J., Translating solitons to symplectic mean curvature flows, Ann. Global Anal. Geom., 38(2), 2010, 161–169] to higher dimension.
Keywords
Rigidity
/
Lagrangian translating solitons
/
Lagrangian angle
/
Mean curvature
Cite this article
Download citation ▾
Hongbing Qiu, Chenyu Zhu.
A Note on Translating Solitons to Lagrangian Mean Curvature Flows.
Chinese Annals of Mathematics, Series B, 2025, 46(3): 443-448 DOI:10.1007/s11401-025-0024-1
| [1] |
Castro, I. and Lerma, A. M., Translating solitons for Lagrangian mean curvature flow in complex Euclidean plane, Internat. J. Math., 23(10), 2012, 16 pp.
|
| [2] |
CastroI, LermaA MLagrangian translators under mean curvature flow, 2015
|
| [3] |
ChenJ, LiJ. Singularity of mean curvature flow of Lagrangian submanifolds. Invent. Math., 2004, 156(1): 25-51
|
| [4] |
ChenQ, QiuH. Rigidity of self-shrinkers and translating solitons of mean curvature flows. Adv. Math., 2016, 294: 517-531
|
| [5] |
Cooper, A. A., Singularities of the Lagrangian mean curvature flow, 2015, arXiv:1505.01856.
|
| [6] |
HanX, LiJ. Translating solitons to symplectic and Lagrangian mean curvature flows. Internat. J. Math., 2009, 20(4): 443-458
|
| [7] |
HanX, SunJ. Translating solitons to symplectic mean curvature flows. Ann. Global Anal. Geom., 2010, 38(2): 161-169
|
| [8] |
HuiskenG. Flow by mean curvature of convex surfaces into spheres. J. Differential Geom., 1984, 20(1): 237-266
|
| [9] |
HuiskenG. Asymptotic behavior for singularities of the mean curvature flow. J. Differential Geom., 1990, 31(1): 285-299
|
| [10] |
JoyceD, LeeY-I, TsuiM-P. Self-similar solutions and translating solitons for Lagrangian mean curvature flow. J. Differential Geom., 2010, 84(1): 127-161
|
| [11] |
LiX, LiuY, QiaoR. A uniqueness theorem of complete Lagrangian translator in ℂ2. Manuscripta Math., 2021, 164(1–2): 251-265
|
| [12] |
NevesA. Singularities of Lagrangian mean curvature flow: Zero-Maslov class case. Invent. Math., 2007, 168(3): 449-484
|
| [13] |
NevesA, TianG. Translating solutions to Lagrangian mean curvature flow. Trans. Amer. Math. Soc., 2013, 365(11): 5655-5680
|
| [14] |
Qiu, H. B., Rigidity of symplectic translating solitons, J. Geom. Anal., 32(11), 2022, 19 pp.
|
| [15] |
Qiu, H. B., A Bernstein type result of translating solitons, Calc. Var. Partial Differential Equations, 61(6), 2022, 9 pp.
|
| [16] |
SchoenR, WolfsonJ. Minimizing area among Lagrangian surfaces: The mapping problem. J. Differential Geom., 2001, 58: 1-86
|
| [17] |
Smoczyk, K., A canonical way to deform a Lagrangian submanifold, 1996, arXiv:dg-ga/9605005.
|
| [18] |
SmoczykKThe Lagrangian mean curvature flow, 2000, Leipzig, Univ. Leipzig (Habil.-Schr.)(Der Lagrangesche mittlere Krmmungsfluss)
|
| [19] |
Smoczyk, K., Local non-collapsing of volume for the Lagrangian mean curvature flow, Calc. Var. Partial Differential Equations, 58(1), 2019, 14 pp.
|
| [20] |
SunJ. A gap theorem for translating solitons to Lagrangian mean curvature flow. Differential Geom. Appl., 2013, 31(5): 568-576
|
| [21] |
SunJ. Mean curvature decay in symplectic and Lagrangian translating solitons. Geom. Dedicata, 2014, 172: 207-215
|
| [22] |
SunJ. Rigidity results on Lagrangian and symplectic translating solitons. Commun. Math. Stat., 2015, 3(1): 63-68
|
| [23] |
WangM-T. Mean curvature flow of surfaces in Einstein four-manifolds. J. Differential Geom., 2001, 57(2): 301-338
|
| [24] |
XinY L. Translating solitons of the mean curvature flow. Calc. Var. Partial Differential Equations, 2015, 54: 1995-2016
|
RIGHTS & PERMISSIONS
The Editorial Office of CAM and Springer-Verlag Berlin Heidelberg
