6533b871fe1ef96bd12d17bb
RESEARCH PRODUCT
Mean curvature flow of graphs in warped products
Vicente F. Miquel MolinaA. A. Borisenkosubject
Mean curvature flowPure mathematicsMean curvatureApplied MathematicsGeneral MathematicsMathematical analysisRiemannian manifoldLipschitz continuityCurvatureGraphHypersurfaceMathematics::Differential GeometryMathematicsScalar curvaturedescription
Let M be a complete Riemannian manifold which either is compact or has a pole, and let φ be a positive smooth function on M . In the warped product M ×φ R, we study the flow by the mean curvature of a locally Lipschitz continuous graph on M and prove that the flow exists for all time and that the evolving hypersurface is C∞ for t > 0 and is a graph for all t. Moreover, under certain conditions, the flow has a well defined limit.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2012-09-01 | Transactions of the American Mathematical Society |