arXiv research

Extends p-harmonic map theory for new properties.

Sharp inequality for $p$-harmonic maps with new optimal constant.

The study finds infinitely many p-harmonic maps between spheres for specific p and m.

The paper estimates gradients and proves Liouville theorems for p-harmonic maps.

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

The study proves smoothness and estimates for $p$-harmonic mappings between Riemannian manifolds.

Global existence and convergence of heat flow for p-harmonic maps.

The paper proves a Liouville theorem for a specific type of harmonic maps on foliated manifolds.

We prove that, in general, given a $p$-harmonic map $F:M\to N$ and a convex function $H:N\to\mathbb{R}$, the composition $H\circ F$ is not $p$-subharmonic. By assuming some rotational symmetry on manifolds and functions, we reduce the problem to an ordinary differential inequality. The key of the proof is an asymptotic…

The paper proves vanishing and finiteness theorems for p-harmonic 1-forms.

We introduce and study an approximate solution of the p-Laplace equation, and a linearlization $L_ε$ of a perturbed p-Laplace operator. By deriving an $L_ε$-type Bochner's formula and a Kato type inequality, we prove a Liouville type theorem for weakly p-harmonic functions with finite p-energy on a complete noncompact …

Researchers extend regularity of $p$-harmonic maps into spheres for a new range of $p$.

Study cohomology classes related to harmonic maps on submersions.

The paper investigates Liouville type theorems for various harmonic forms on Riemannian manifolds.

We prove a general comparison result for homotopic finite $p$-energy $C^{1}$ $p$-harmonic maps $u,v:M\to N$ between Riemannian manifolds, assuming that $M$ is $p$-parabolic and $N$ is complete and non-positively curved. In particular, we construct a homotopy through constant $p$-energy maps, which turn out to be $p$-ha…

We study a second order ordinary differential equation corresponding to rotationally symmetric $p$-harmonic maps. We show unique continuation and Liouville's type theorems for positive solutions. We discuss the existence of bounded positive entire solutions. Asymptotic properties of the positive solutions are investiga…

Unified proof of monotonicity for p-harmonic forms and connections.

The study examines the behavior of $p$-harmonic maps to $S^1$ as $p$ approaches 2.

In p-harmonic coordinates, Hölder metrics lead to useful gauge conditions in conformal geometry.

Proves existence of maximizers for eigenvalue optimization on manifolds.

Harmonic morphisms and p-harmonic functions constructed on symmetric spaces.

Adapting \cite{strz3}, we define generalized $p$-harmonic maps into Riemannian homogeneous targets, a notion of solutions not belonging to the energy space. Restricting our attention to the subcritical range $p$ greater than the domain dimension $n$, we show a uniform $C^{1,α}$-regularity result for a sequence of such …

Equivalence of conformal maps proved in sub-Riemannian manifolds.

In this note, we investigate estimates of the Morse index for F-harmonic maps into spheres, our results extend partially those obtained in ([14]) and ([15]) for harmonic and p-harmonic maps.

In this two papers we deal with the relative homotopy Dirichlet problem for p-harmonic maps from compact manifolds with boundary to manifolds of non-positive sectional curvature. Notably, we give a complete solution to the problem in case the target manifold is either compact and a new proof in case it is rotationally …

In this note, we show that some F-harmonic maps into spheres are global maxima of the variations of their energy functional on the conformal group of the sphere. Our result extends partially those obtained in [15] and [17] for harmonic and p-harmonic maps.

The paper studies geometric properties of $Φ_{(3)}$-harmonic maps and proves Liouville type results.

Constructs explicit $p$-harmonic functions on Grassmannians and flag manifolds.

Let $p$ be a real number greater number greater than one. Suppose that a graph $G$ of bounded degree is quasi-isometric with a Riemannian manifold $M$ with certain properties. Under these conditions we will show that the $p$-harmonic boundary of $G$ is homeomorphic to the $p$-harmonic boundary of $M$. We will also prov…

Paper solves Minkowski problem for p-harmonic measures.

The paper provides new examples of $p$-harmonic functions using isoparametric foliations.

Let $p$ be a real number greater than one and let $G$ be a connected graph of bounded degree. In this paper we introduce the $p$-harmonic boundary of $G$. We use this boundary to characterize the graphs $G$ for which the constant functions are the only $p$-harmonic functions on $G$. It is shown that any continuous func…

The paper proves vanishing properties of $p$-harmonic $\ell$-forms on various Riemannian manifolds.

Constructs explicit p-harmonic functions on specific Lie groups.

In this article, we study the regularity of minimizing and stationary $p$-harmonic maps between Riemannian manifolds. The aim is obtaining Minkowski-type volume estimates on the singular set $S(f)=\{x \ \ s.t. \ \ f \text{ is not continuous at } x\}$, as opposed to the weaker and non quantitative Hausdorff dimension bo…

New p-harmonic and harmonic morphisms found on Lie groups.

$\infty$-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 E…

Derives monotonic quantities for $p$-harmonic functions on manifolds.

The abstract discusses p-harmonic forms and their geometric properties, proving new theorems about Lp-cohomology.

Constructs explicit harmonic functions and morphisms on complex and quaternionic Grassmannians.

New method constructs explicit $p$-harmonic functions on Lie groups.

Researchers create explicit p-harmonic functions on specific symmetric spaces.

Study finds nontrivial $n$-harmonic maps from $S^n$ to closed manifolds.

Derives new monotone quantities for p-harmonic functions on asymptotically flat 3-manifolds.

Study cohomology classes related to $n$-harmonic morphisms and $F$-harmonic maps.

Estimates for harmonic functions in curved spaces.

Extends strong comparison principle for p-harmonic functions in Carnot-Caratheodory spaces.

Study connectedness at infinity using p-harmonic functions.