Stable shredded spheres and causal random maps with large faces

Scaling limits of random planar maps with large faces

We discuss asymptotics for large random planar maps under the assumption that the distribution of the degree of a typical face is in the domain of attraction of a stable distribution with index α ∈ (1, 2). When the number n of vertices of the map tends to infinity, the asymptotic behavior of distances from a distinguished vertex is described by a random process called the continuous distance pr...

Stable Stationary Harmonic Maps to Spheres

Dedicated to Professor WeiYue Ding on the occasion of his 60th birthday Abstract For k ≥ 3, we establish new estimate on Hausdorff dimensions of the singular set of stable-stationary harmonic maps to the sphere S. We show that the singular set of stable-stationary harmonic maps from B to S is the union of finitely many isolated singular points and finitely many Hölder continuous curves. We also...

Relative Compactness and Product Stable Quotient Maps

C*-Extreme Points and C*-Faces oF the Epigraph iF C*-Affine Maps in *-Rings

Abstract. In this paper, we define the notion of C*-affine maps in the unital *-rings and we investigate the C*-extreme points of the graph and epigraph of such maps. We show that for a C*-convex map f on a unital *-ring R satisfying the positive square root axiom with an additional condition, the graph of f is a C*-face of the epigraph of f. Moreover, we prove som...

Stable Exponentially Harmonic Maps Between Finsler Manifolds