TY - JOUR
T1 - Mean curvature flow closes open ends of noncompact surfaces of rotation
AU - Giga, Yoshikazu
AU - Seki, Yukihiro
AU - Umeda, Noriaki
N1 - Funding Information:
The authors are sincerely grateful to Dr. Takeshi Ohtsuka for reading manuscripts and giving valuable advice. The work of Y. Giga was partly supported by the Grant-in-Aid for Scientific Research, No. 20654017, No. 18204011, the Japan Society of the Promotion of Science (JSPS) and by COE Program “Mathematics of Nonlinear Structures via Singularities” sponsored by JSPS. Research by Y. Seki was supported by Research Fellowships of JSPS. Much of the work of N. Umeda was done while he visited the University of Tokyo during 2005–2009 as a postdoctoral fellow. Its hospitality is gratefully acknowledged as well as the support from formation of COE “New Mathematical Development Center to Support Scientific Technology” during 2005–2008 and COE “The research and training center for new development in mathematics” in 2009, supported by JSPS.
Publisher Copyright:
© Taylor & Francis Group, LLC.
PY - 2009
Y1 - 2009
N2 - We discuss the motion of noncompact axisymmetric hypersurfaces Γt evolved by mean curvature flow. Our study provides a class of hypersurfaces that share the same quenching time with the shrinking cylinder evolved by the flow and prove that they tend to a smooth hypersurface having no pinching neck and having closed ends at infinity of the axis of rotation as the quenching time is approached. Moreover, they are completely characterized by a condition on initial hypersurface.
AB - We discuss the motion of noncompact axisymmetric hypersurfaces Γt evolved by mean curvature flow. Our study provides a class of hypersurfaces that share the same quenching time with the shrinking cylinder evolved by the flow and prove that they tend to a smooth hypersurface having no pinching neck and having closed ends at infinity of the axis of rotation as the quenching time is approached. Moreover, they are completely characterized by a condition on initial hypersurface.
UR - http://www.scopus.com/inward/record.url?scp=74949083849&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=74949083849&partnerID=8YFLogxK
U2 - 10.1080/03605300903296926
DO - 10.1080/03605300903296926
M3 - Article
AN - SCOPUS:74949083849
SN - 0360-5302
VL - 34
SP - 1508
EP - 1529
JO - Communications in Partial Differential Equations
JF - Communications in Partial Differential Equations
IS - 11
ER -