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Ye-Lin Ou

Publications and source records attributed to Ye-Lin Ou.

40 records · Page 3Linked to original sources
arXiv2009

Biharmonic hypersurfaces in Riemannian manifolds

We study biharmonic hypersurfaces in a generic Riemannian manifold. We first derive an invariant equation for such hypersurfaces generalizing the biharmonic hypersurface equation in space forms studied in \cite{Ji2}, \cite{CH}, \cite{CMO1}, \cite{CMO2}. We then apply the equation to show that the generalized Chen's conjecture is true for totally umbilical biharmonic hypersurfaces in an Einstein space, and construct a (2-parameter) family of conformally flat metrics and a (4-parameter) family of multiply warped product metrics each of which turns the foliation of an upper-half space of $\mathhbb{R}^m$ by parallel hyperplanes into a foliation with each leave a proper biharmonic hypersurface. We also characterize proper biharmonic vertical cylinders in $S^2\times \mathbb{R}$ and $H^2\times \mathbb{R}$.

math.DG↗
arXiv2008

On conformal biharmonic immersions

This paper studies conformal biharmonic immersions. We first study the transformations of Jacobi operator and the bitension field under conformal change of metrics. We then obtain an invariant equation for a conformal biharmonic immersion of a surface into Euclidean 3-space. As applications, we construct a 2-parameter family of non-minimal conformal biharmonic immersions of cylinder into $\r^3$ and some examples of conformal biharmonic immersions of 4-dimensional Euclidean space into sphere and hyperbolic space thus provide many simple examples of proper biharmonic maps with rich geometric meanings. These suggest that there are abundant proper biharmonic maps in the family of conformal immersions. We also explore the relationship between biharmonicity and holomorphicity of conformal immersions of surfaces.

math.DG↗
arXiv2007

Some classifications of \infty-Harmonic maps between Riemannian manifolds

$\infty$-Harmonic maps are a generalization of $\infty$-harmonic functions. They can be viewed as the limiting cases of p-harmonic maps as p goes to infinity. In this paper, we give complete classifications of linear and quadratic $\infty$-harmonic maps from and into a sphere, quadratic $\infty$-harmonic maps between Euclidean spaces. We describe all linear and quadratic $\infty$-harmonic maps between Nil and Euclidean spaces, between Sol and Euclidean spaces. We also study holomorphic $\infty$-harmonic maps between complex Euclidean spaces.

math.DG↗