Advanced Institute for Materials Research (AIMR), Tohoku University

[9] Keita Kunikawa

**On Ecker's local integral quantity at infinity for ancient mean curvature flows**.

To appear in Ann. Global Anal. Geom.

arXiv:2005.09845.

[8] Keita Kunikawa; Yohei Sakurai

**Liouville theorem for heat equation along ancient super Ricci flow via reduced geometry**.

arXiv:2005.04882.

[7] Keita Kunikawa; Ryosuke Takahashi

**Convergence of mean curvature flow in hyper-Kähler manifolds**.

Pacific J. Math., Vol. 305 (2020), No. 2, 667-691.

arXiv:1808.06997.

[6] Keita Kunikawa; Shunsuke Saito

**Remarks on topology of stable translating solitons**.

Geom. Dedicata., Vol. 202 (2019), No. 1, 1-8.

arXiv:1804.05463.

[5] Toru Kajigaya; Keita Kunikawa

**Hamiltonian stability for weighted measure and generalized Lagrangian mean curvature flow**.

J. Geom. Phys., Vol. 128 (2018), 140-168.

arXiv:1710.05537.

[4] Keita Kunikawa

**Non-existence of eternal solutions to Lagrangian mean curvature flow with non-negative Ricci curvature**.

Geom. Dedicata., Vol. 201 (2019), No. 1, 369-377.

arXiv:1611.03594.

[3] Keita Kunikawa

**Translating solitons in arbitrary codimension**.

Asian J. Math., Vol.21 (2017), No. 5, 855-872.

[2] Keita Kunikawa

**A Bernstein type theorem of ancient solutions to the mean curvature flow**.

Proc. Amer. Math. Soc., Vol.144 (2016), 1325-1333.

[1] Keita Kunikawa

**Bernstein-type theorem of translating solitons in arbitrary codimension with flat normal bundle**.

Calc. Var. Partial Differential Equations, Vol.54 (2015), No. 2, 1331-1344.

[6] Keita Kunikawa

**Convergence of mean curvature flow in hyperkähler manifolds**.

Submanifolds in Yuzawa 2018, Conference paper.

[5] Toru Kajigaya; Keita Kunikawa

**Convergence of generalized Lagrangian mean curvature flow in Fano manifolds**.

Joint work with Toru Kajigaya.

RIMS Kokyuroku, No. 2068 1-21.

[4] Keita Kunikawa

**Rigidity theorem for eternal solutions to Lagrangian mean curvature flow**.

Conference on Differential Geometry at Fukuoka University 2016, Conference paper.

[3] Keita Kunikawa

**Translating solitons in arbitrary codimension**.

Submanifolds in Yuzawa 2015, Conference paper.

[2] Keita Kunikawa

** Nonexistence theorem for eternal solutions to mean curvature flow**.

Conference on Differential Geometry at Fukuoka University 2015, Conference paper.

[1] Keita Kunikawa

**Translating solitons of mean curvature flow in arbitrary codimension**.

Submanifold geometry and Lie group actions 2015, Conference paper.

**Title**: __Translating Solitons of the Mean Curvature Flow in Arbitrary Codimension__

**Abstract**: In the thesis we study the translating solitons of the mean curvature flow.
Although many researchers study translating solitons in codimension one, there are few references and examples for higher codimensional case.
Here, we mainly consider the mean curvature lfow in arbitrary codimension.
Firstly, we obtain non-existence results of Bernstein type for the translating solitons in higher codimension and the eternal solutions in codimension one.
Secondly we provide many new examples of translating solitons in arbitrary codimension. We will see that these examples have the property called parallel principal normal. Finally we characterize the complete translating solitons with parallel principal normal under a certain curvature condition.

**Summary**: PDF