TY - JOUR
T1 - The harmonic mean curvature flow of nonconvex surfaces in ℝ3
AU - Daskalopoulos, Panagiota
AU - Sesum, Natasa
N1 - Funding Information:
P. Daskalopoulos was partially supported by NSF Grants 0701045 and 0354639 and N. Sesum was partially supported by NSF Grant 0604657.
PY - 2009/11
Y1 - 2009/11
N2 - We consider a compact star-shaped mean convex hypersurface. We prove that in some cases the flow exists until it shrinks to a point. We also prove that in the case of a surface of revolution which is star-shaped and mean convex, a smooth solution always exists up to some finite time T < ∞ at which the flow shrinks to a point asymptotically spherically.
AB - We consider a compact star-shaped mean convex hypersurface. We prove that in some cases the flow exists until it shrinks to a point. We also prove that in the case of a surface of revolution which is star-shaped and mean convex, a smooth solution always exists up to some finite time T < ∞ at which the flow shrinks to a point asymptotically spherically.
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U2 - 10.1007/s00526-009-0258-x
DO - 10.1007/s00526-009-0258-x
M3 - Article
AN - SCOPUS:70450230536
SN - 0944-2669
VL - 37
SP - 187
EP - 215
JO - Calculus of Variations and Partial Differential Equations
JF - Calculus of Variations and Partial Differential Equations
IS - 1
ER -