On the existence of a closed, embedded, rotational $$\lambda $$-hypersurface

Ross, John

doi:10.1007/s00022-019-0483-1

Cited by 13 publications

(7 citation statements)

References 2 publications

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“…(1.3), self-shrinkers of constant λ were studied independently by Cheng and Wei [7] and McGonagle and Ross [17]. Since then, and if α = −1/2, these surfaces have received the interest for geometers: [4][5][6]12,19,20].…”

Section: Introduction and Statement Of The Resultsmentioning

confidence: 99%

Ruled Surfaces of Generalized Self-Similar Solutions of the Mean Curvature Flow

López

2021

Mediterr. J. Math.

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In Euclidean space, we investigate surfaces whose mean curvature H satisfies the equation $$H=\alpha \langle N,{\mathbf {x}}\rangle +\lambda $$ H = α ⟨ N , x ⟩ + λ , where N is the Gauss map, $${\mathbf {x}}$$ x is the position vector, and $$\alpha $$ α and $$\lambda $$ λ are two constants. There surfaces generalize self-shrinkers and self-expanders of the mean curvature flow. We classify the ruled surfaces and the translation surfaces, proving that they are cylindrical surfaces.

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Section: Introduction and Statement Of The Resultsmentioning

confidence: 99%

Ruled Surfaces of Generalized Self-Similar Solutions of the Mean Curvature Flow

López

2021

Mediterr. J. Math.

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“…When α = −1/2 in equation (3), self-shrinkers of constant λ were studied independently by Cheng and Wei ( [7]) and McGonagle and Ross ([17]). Since then, and if α = −1/2, these surfaces have received the interest for geometers: [4,5,6,12,19,20].…”

Section: Introduction and Statement Of The Resultsmentioning

confidence: 99%

Ruled surfaces of generalized self-similar solutions of the mean curvature flow

López¹

2020

Preprint

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“…Let SO(n) denote the special orthogonal group and act on R n+1 = {(x, y) : x ∈ R, y ∈ R n } in the usual way, then we can identify the space of orbits R n+1 /SO(n) with the half plane H = (x, r) ∈ R 2 : x ∈ R, r ≥ 0 under the projection(see [12])…”

Section: Preliminariesmentioning

confidence: 99%

“…In [5], Cheng and Wei constructed the first nontrivial example of a λ-hypersurface which is diffeomorphic to S n−1 × S 1 using techniques similar to Angenent [1]. In [12], using a similar method to McGrath [10], Ross constructed a λ-hypersurface in R 2n+2 which is diffeomorphic to S n × S n × S 1 and exhibits a SO(n) × SO(n) rotational symmetry. In [9], Li and Wei constructed an immersed S n λ-hypersurface using a similar method to [7].…”

Section: Introductionmentioning

confidence: 99%