• Corpus ID: 248496114

Examples of compact embedded $\lambda$-hypersurfaces

  title={Examples of compact embedded \$\lambda\$-hypersurfaces},
  author={Qing-ming Cheng and Junqi Lai and Guoxin Wei},
. In the paper, we construct compact embedded λ -hypersurfaces which are diffeomorphic to a sphere and are not isometric to a standard sphere. Hence, one can not expect to have Alexandrov type theorem for λ -hypersurfaces. 



Examples of compact λ-hypersurfaces in Euclidean spaces

In this paper, we first construct compact embedded λ-hypersurfaces with the topology of torus which are called λ-torus in Euclidean spaces ℝ n +1 . Then, we give many compact immersed λ-hypersurfaces

On the existence of a closed, embedded, rotational λ -hypersurface

. In this paper we show the existence of a closed, embedded λ hypersurfaces Σ ⊂ R 2 n . The hypersurface Σ is diffeomorphic to S n − 1 × S n − 1 × S 1 and exhibits SO ( n ) × SO ( n ) symmetry. Our

Embedded self-similar shrinkers of genus 0

We confirm a well-known conjecture that the round sphere is the only compact, embedded self-similar shrinking solution to the mean curvature flow with genus $0$. More generally, we show that the only

Complete λ -hypersurfaces of weighted volume-preserving mean curvature flow

In this paper, we introduce a special class of hypersurfaces which are called λ hypersurfaces related to a weighted volume preserving mean curvature flow in the Euclidean space. We prove that λ

Immersed self-shrinkers

We construct infinitely many complete, immersed self-shrinkers with rotational symmetry for each of the following topological types: the sphere, the plane, the cylinder, and the torus.

The hyperplane is the only stable, smooth solution to the Isoperimetric Problem in Gaussian space

We study stable, two-sided, smooth, properly immersed solutions to the Gaussian Isoperimetric Problem. That is, we study hyper-surfaces $$\Sigma ^n \subset {{\mathbb {R}}}^{n+1}$$Σn⊂Rn+1 that are

Complete λ-hypersurfaces of weighted volume-preserving mean curvature flow, Cal

  • Var. Partial Differential Equations
  • 2018

Closed Mean Curvature Self-Shrinking Surfaces of Generalized Rotational Type

For each $n\geq 2$ we construct a new closed embedded mean curvature self-shrinking hypersurface in $\mathbb{R}^{2n}$. These self-shrinkers are diffeomorphic to $S^{n-1}\times S^{n-1}\times S^1$ and

1-dimensional solutions of the λ-self shrinkers

  • Geom. Dedicata
  • 2017