Abstract
Let F0: M → ℝn+1 be a smooth immersion of an n-dimensional hypersurface in Euclidean space, n ≥ 1. The evolution of M0=F0(M) by mean curvature flow is a one-parameter family of immersions F: M x [0, T → ℝn+1 satisfying
where H(p, t) and υH(p, t) are respectively the mean curvature and the normal at the point F(p, t) of the surface M t =F(·, t)(M).
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2010 Birkhäuser Verlag
About this chapter
Cite this chapter
Ritoré, M., Sinestrari, C. (2010). Introduction. In: Mean Curvature Flow and Isoperimetric Inequalities. Advanced Courses in Mathematics — CRM Barcelona. Birkhäuser Basel. https://doi.org/10.1007/978-3-0346-0213-6_1
Download citation
DOI: https://doi.org/10.1007/978-3-0346-0213-6_1
Publisher Name: Birkhäuser Basel
Print ISBN: 978-3-0346-0212-9
Online ISBN: 978-3-0346-0213-6
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)