arXiv research

The paper explores p-biharmonic hypersurfaces in Einstein and conformally flat spaces.

Paper defines p-biharmonic submanifolds and stress tensors in space forms.

Extends $p$-biharmonic and bi-$p$-harmonic map definitions.

Study on p-biharmonic maps from gradient Ricci solitons, focusing on 2D cigar soliton.

Study of $p$-biharmonic curves and their properties.

Let $u: (M, g)\to (N, h)$ be a map between Riemannian manifolds $(M, g)$ and $(N, h)$. The $p$-bienergy of $u$ is defined by $E_p(u)=\int_M|τ(u)|^pdν_g$, where $τ(u)$ is the tension field of $u$ and $p>1$. Critical points of $E_p(\cdot)$ are called $p$-biharmonic maps. In this paper we will prove nonexistence result of…

Extends biharmonic concepts to new hypersurfaces and curves.

Extends p-harmonic map theory for new properties.

In this note we consider the Liouville type theorem for a properly immersed submanifold $M$ in a complete Riemmanian manifold $N$. Assume that the sectional curvature $K^N$ of $N$ satisfies $K^N\geq-L(1+dist_N(\cdot,q_0)^2)^\fracα{2}$ for some $L>0, 2>α\geq 0$ and $q_0\in N$. (i) If $Δ|\vec{H}|^{2p-2}\geq k|\vec{H}|^{2…