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We study Finsler metrics with orthogonal invariance. By determining an expression of these Finsler metrics we find a PDE equivalent to these metrics being locally projectively flat. After investigating this PDE we manufacture projectively flat Finsler metrics with orthogonal invariance in terms of error functions.

Pseudo-immersions superminimales d'une surface de Riemann dans une variété riemannienne de dimension 4

P. Gauduchon (1986)

Bulletin de la Société Mathématique de France

Quadratic harmonic morphisms and O-systems

Ye-Lin Ou (1997)

Annales de l'institut Fourier

We introduce O-systems (Definition 3.1) of orthogonal transformations of $ℝ^{m}$ , and establish $ℝ$ correspondences both between equivalence classes of Clifford systems and those of O-systems, and between O-systems and orthogonal multiplications of the form $μ : ℝ^{n} \times ℝ^{m} \to ℝ^{m}$ , which allow us to solve the existence problems both for $O$ -systems and for umbilical quadratic harmonic morphisms simultaneously. The existence problem for general quadratic harmonic morphisms is then solved by the Splitting Lemma. We also study properties...

Quaternionic geometry of a nilpotent variety.

Andrew Swann, Piotr Z. Kobak (1993)

Mathematische Annalen

Quaternionic maps and minimal surfaces

Jingyi Chen, Jiayu Li (2005)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

Let $(M, J^{α}, α = 1, 2, 3)$ and $(N, 𝒥^{α}, α = 1, 2, 3)$ be hyperkähler manifolds. We study stationary quaternionic maps between $M$ and $N$ . We first show that if there are no holomorphic 2-spheres in the target then any sequence of stationary quaternionic maps with bounded energy subconverges to a stationary quaternionic map strongly in $W^{1, 2} (M, N)$ . We then find that certain tangent maps of quaternionic maps give rise to an interesting minimal 2-sphere. At last we construct a stationary quaternionic map with a codimension-3 singular set by using the embedded...

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Perturbing away singularities of Harmonic Maps.

p-harmonic maps and minimal submanifolds.

P-Harmonic obstacle problems.

Phenomena of compensation and estimates for partial differential equations.

Principe de Dirichlet pour les formes différentielles

Principe de Dirichlet pour les formes différentielles

Projectively flat Finsler metrics with orthogonal invariance

Pseudo-immersions superminimales d'une surface de Riemann dans une variété riemannienne de dimension 4

Quadratic harmonic morphisms and O-systems

Quaternionic geometry of a nilpotent variety.

Quaternionic maps and minimal surfaces

Recent existence and regularity results for wave maps

Regularity and uniqueness of harmonic maps into and ellipsoid.

Regularity at the free boundary of two-dimensional stationary harmonic maps

Regularity for a non linear variational problem in dimension two.

Regularity of a Minimal Surface at its Free Boundary.

Regularity of minimizing harmonic maps into S4, S5 and symmetric spaces.

Regularity of minimizing harmonic maps into the sphere.

Regularity of Minimzing Harmonic Mappings into ellipsoids and similar other manifolds.

Regularity of p-harmonic maps from the p-dimensional ball into a sphere.

Currently displaying 221 – 240 of 313