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MMinimal hypersurfaces asymptotic to Simons cones Laurent Mazet ∗ Abstract In this paper we prove that up to similarity there are only twominimal hypersurfaces in R n 2 that are asymptotic to a Simons cone the minimal cone over the minimal hypersurface cid 112 pn S p × cid 113 n − pn S n − p of S n 1 Mathematical Subject Classification 49F10 53A10

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Minimal hypersurfaces asymptotic to Simons cones By Laurent Mazet Abstract In this paper we prove that up to similarity there are only two minimal hypersurfaces in $mathbb{R}^{n 2}$ that are asymptotic to a Simons cone the minimal cone over the minimal hypersurface $sqrt{frac pn}mathbb{S}^ptimes sqrt{frac{n p}n} mathbb{S

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This cone Cis called a limit cone of we also say that is asymptotic to C A priori the cone Cdepends on the chosen sequence t i and is not smooth outside the origin As an example if is a catenoid 1 = 2 and Cis a plane with multiplicity 2 Notice that in dimension 3 n= 1 except the plane no minimal cone is smooth outside the origin

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in RnC2 that are asymptotic to a Simons cone the minimal cone over the minimal hypersurface q p n S p n p n S n p of SnC1 Keywords minimal hypersurfaces Simons cone 2024 Mathematics subject classi cation Primary 49F10 Secondary 53A10 1 Introduction One important property of minimal hypersurfaces is the monotonicity formula If is a

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