The aim of this paper is to investigate a new link between integrable systems and minimal surface theory. The dressing operation uses the associated family of flat connections of a harmonic map to construct new harmonic maps. Since a minimal surfa...

A super-conformal map is a conformal map from a two-dimensional Riemannian manifold to the Euclidean four-space such that the ellipse of curvature is a circle. Quaternionic holomorphic geometry connects super-conformal maps with holomorphic maps. ...

Simple factor dressing and the Lopez-Ros deformation of minimal surfaces in Euclidean 3-space

Moriya,Katsuhiro;Leschke,,Katrin

arXiv.org 1409.5286 Sep 2014

The aim of this paper is to give a new link between integrable systems and minimal surface theory. The dressing operation uses the associated family of flat connections of a harmonic map to construct new harmonic maps. Since a minimal surface in 3...

Description of a mean curvature sphere of a surface by quaternionic holomorphic geometry (Submanifolds and Quaternion structure 2012/06/25-27)

ADVANCES IN APPLIED CLIFFORD ALGEBRAS 27(2) 1243-1262 Jun 2017 [Refereed]

A conformal map from a Riemann surface to the Euclidean four-space is explained in terms of its twistor lift. A local factorization of a differential of a conformal map is obtained. As an application, the factorization of a differential provides a...

The Schwarz lemma for conformal maps from the open unit disk into the Euclidean four-space[Invited]

Moriya,Katsuhiro

Geometry of Submanifolds and Integrable Systems 26 Mar 2018 Yoshihiro Ohnita, Martin Guest, Young Jin Suh, Masaaki Umehara, Wayne Rossman, Takashi Sakai, Masashi Yasumoto

The Schwarz lemma is an inequality about the norms of holomorphic functions on the open unit disk. We give a similar inequality about the norms of conformal maps from the open unit disk into the Euclidean four-space

Complex structures of vector bundles and harmonic maps into a sphere[Invited]

守屋,克洋

Submanifolds at Yuzawa 2017 30 Nov 2017 間下克哉、田崎博之、入江博、酒井高司

The Weierstrass representation for surfaces in Euclidean space of arbitrary dimension

Moriya,Katsuhiro

2016 Mathematical Society of Japan, Autumn meeting 15 Sep 2016 日本数学会

The Schwarz lemma for super-conformal maps[Invited]

Moriya,Katsuhiro

The 20th International Workshop on Hermitian Symmetric Spaces and Submanifolds 26 Jul 2016 Young Jin Suh, Yoshihiro Ohnita, Jiazu Zhou, Byung Hak Kim

A super-conformal map from a Riemann surface to the Euclidean four-space is a surface with circular ellipse of curvature with respect to the induced metric. This map has properties similar to the holomorphic function on a Riemann surface. In this ...

Twistor lifts and factorization for conformal maps of a surface

Moriya,Katsuhiro

The 4th Workshop "Complex Geometry and Lie Groups" 22 Mar 2016 Anna Fino, Ryushi Goto, Keizo Hasegawa, Jun-ichi Matsuzawa

Conformal maps from a Riemann surface to the four-dimensional Eu- clidean space are studied by twistor lifts and a quaternionic holomorphic struc- ture. We explain a relation between these objects and define a factorization of the differential of ...

Project Year: Sep 2016 - Aug 2018 Investigator(s): Katrin Leschke

Led by Dr Katrin Leschke at the University of Leicester, Department of Mathematics; m:iv brings together researchers at five international institutions to work on the study of minimal surfaces: combining the expertise of the network partners in th...

Japan Society of for the Promotion of Science: Grant-in-Aid for Scientific Research (C)

Project Year: Apr 2013 - Mar 2017 Investigator(s): Katsuhiro Moriya

A holomorphic function relates a figure in the plane to a figure in the plane
without changing the angle. This is said that a holomorphic function is conformal. A holomorphic function has mathematically good properties.
If a map relates a figure i...

Japan Society of for the Promotion of Science: Grant-in-Aid for Scientific Research (C)

Project Year: Apr 2010 - Mar 2012 Investigator(s): Katsuhiro Moriya

The correspondence between the Lopez-Ros deformation of a minimal surface in Euclidean (four-)space and the dressing transformations of two families of flat connections associated with a minimal surface was cleared by the joint work with Dr, Katri...

A member of the organising committee of Minimal surfaces and related topics, m:iv winter 2018 workshop at Granada University in Spain. http://gigda.ugr.es/minimal2018

Mar 2017

A member of the organising committee of m:iv spring 2017 workshop at University College Cork in Ireland.
http://www2.le.ac.uk/projects/miv/workshop-programme/spring-2017-workshop

Sep 2016

A network partner of the m:iv minimal surfaces: integrable systems and visualisation.
An international research group funded by The Leverhulme Trust.
Led by Dr Katrin Leschke at the University of Leicester, Department of Mathematics; m:iv brings together researchers at five international institutions to work on the study of minimal surfaces: combining the expertise of the network partners in the areas of visualisation, minimal surfaces and integrable systems will allow new approaches in this research area. The network will run a series of seminars, ranging from introductory presentations to detailed talks on specialised results. The seminar series will develop the necessary foundations for the research whilst computer experiments are undertaken. Extended research visits each year will take place between network partners. In addition to the seminar series and research visits, the network will run a programme of workshops, hosted in turn by each network partner highlighting their area of research, with the final workshop taking place at Leicester, where the various strands will be linked together.
http://www2.le.ac.uk/projects/miv