A Survey of Closed Self-Shrinkers with Symmetry

Drugan, Gregory; Lee, Hojoo; Nguyen, Xuan Hiên

doi:10.1007/s00025-018-0763-3

Cited by 23 publications

(15 citation statements)

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“…The literature in the topic of self-shrinkers is sufficiently large to give a summary. We address the reader to [8,10,15] and references therein as a first approach.…”

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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“…The literature in the topic of self-shrinkers is sufficiently large to give a summary. We address the reader to [8,10,15] and references therein as a first approach.…”

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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show abstract

“…The literature in the topic of selfshrinkers is sufficiently large to give a summary. We address the reader to [8,10,15] and references therein as a first approach.…”

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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“…Concerning a different geometric problem, we recall here that Angenent [2] used the shooting method to construct an embedded, rotationally symmetric, self-shrinking S 1 × S n−1 in R n+1 . Concerning, instead, the contributions we will present in the next section, note that, later, more examples of immersed, rotationally symmetric self-shrinkers were found in [7].…”

Section: Existence Of a Minimally Embedded Hypertorusmentioning

confidence: 99%