Abstract
We study the motion of noncompact hypersurfaces moved by their mean curvature obtained by a rotation around $x$-axis of the graph a function $y=u(x,t)$ (defined for all $x\in \mathbb{R}$). We are interested to estimate its profile when the hypersurface closes open ends at the quenching (pinching) time $T$. We estimate its profile at the quenching time from above and below. We in particular prove that $u(x,T)$ ~ $|x|^{-a}$ as $|x|\to\infty$ if $u(x,0)$ tends to its infimum with algebraic rate $|x|^{-2a} $ (as $|x| \to \infty $ with $a>0$).
Highlights
Introduction and main theoremThis is a continuation of our study [4] on motion of noncompact axisymmetric n-dimensional hypersurface Γt moved by its mean curvature
Let Γt be given by a rotation of the graph of a function y = u(x, t) around the x-axis
In our previous paper [4], among other results, we have proved that if u(x, 0) → m := inf x∈R u(x, 0) > 0 as |x| → ∞, Γt closes open ends at the time T (m), where T (m) is the quenching time of the regular cylinder with radius m
Summary
On decay rate of quenching profile at space infinity for axisymmetric mean curvature flow. Instructions for use Hokkaido University Collection of Scholarly and Academic Papers : HUSCAP. Graduate School of Mathematical Sciences, University of Tokyo, 3-8-1, Komaba, Meguro-ku, Tokyo, 153-8914, Japan
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
