Mean Curvature Evolution of Entire Graphs

Ecker, Klaus; Huisken, Gerhard

doi:10.2307/1971452

Cited by 380 publications

(420 citation statements)

References 3 publications

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“…Ecker and Huisken [5]). Consequently, the argument in step 1 above (with n + 1 replacing n) allows us to conclude P~ fq B n+l(0, 3/4) = 0 (~ < t </3) (3.17)…”

Section: (315)mentioning

confidence: 98%

Motion of level sets by mean curvature III

1992

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“…Ecker and Huisken [5]). Consequently, the argument in step 1 above (with n + 1 replacing n) allows us to conclude P~ fq B n+l(0, 3/4) = 0 (~ < t </3) (3.17)…”

Section: (315)mentioning

confidence: 98%

Motion of level sets by mean curvature III

1992

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“…Gage and Hamilton [17], Grayson [19] study the problem for curves in the plane. In the noncompact case it is shown by Ecker and Huisken in [13] that entire graphs over R n of linear growth 'flatten out'. The interesting question of the formation of singularities in the nonconvex case is considered by Huisken [24], Grayson [20], Dziuk and Kawohl [9], and more recently by Altschuler, Angenent and Giga [1], Ecker [12].…”

Section: (P T) = −(H(p T) − H(t))ν(p T) P ∈mentioning

confidence: 99%

Volume-preserving mean curvature flow of rotationally symmetric surfaces

Athanassenas¹

1997

Comment. Math. Helv.

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Abstract.A rotationally symmetric n-dimensional surface in R n+1 , of enclosed volume V and with boundary in two parallel planes, is evolving under volume-preserving mean curvature flow. For large volume V , we obtain gradient and curvature estimates, leading to long-time existence of the flow, and convergence to a constant mean curvature surface.Mathematics Subject Classification (1991). 35K22, 58G11, 53C21.

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“…Regularity and longtime existence was also obtained for surfaces that can be written as graphs, compare the joint work of the first author with Ecker in [16] and [17].…”

Section: Mean Curvature Flowmentioning

confidence: 83%