A. Ratto

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math.DG2026

Existence and stability of weak critical points of $r$ -energy functionals

Stefano Montaldo, Andrea Ratto, Antonio Sanna

The main aim of this paper is to prove the existence of certain proper weakly $r$ -harmonic ( $E S - r$ -harmonic) maps. We construct critical points which belong to a family of rotation…

math.DG2026

Conformal-biharmonic hypersurfaces in spheres and product spaces

V. Branding, S. Montaldo, S. Nistor +2

The conformal-bienergy functional $E_{2}^{c}$ is a modified version of the classical bienergy functional $E_{2}$ and it is conformally invariant in the case of a four-dimensional domain.…

math.DG2025

Polyharmonic curves in semi-Riemannian manifolds

Stefano Montaldo, Andrea Ratto, Antonio Sanna

Let $(M_{t}^{m}, g)$ be a semi-Riemannian manifold of dimension $m$ with a non-degenerate metric of \textit{index} $t$ , $m \geq 2$ , $1 \leq t \leq m - 1$ . The main aim of this paper is to…

math.DG2024

Polyharmonic helices

Stefano Montaldo, Andrea Ratto

The main aim of this paper is to investigate the existence of Frenet helices which are polyharmonic of order $r$ , shortly, $r$ -harmonic. We shall obtain existence, non-existence an…