Related papers: External geometry of p-minimal surfaces

In this note, we extend the definition of $p$-biharmonic and bi-$p$-harmonic maps between two Riemannian manifolds and explore some of their properties.

We will construct surfaces of revolution with finite total curvature whose Gauss curvatures are not bounded. Such a surface of revolution is employed as a reference surface of comparison theorems in radial curvature geometry. Moreover, we…

We consider minimal maps $f:M\to N$ between Riemannian manifolds $(M,\mathrm{g}_M)$ and $(N,\mathrm{g}_N)$, where $M$ is compact and where the sectional curvatures satisfy $\sec_N\le \sigma\le \sec_M$ for some $\sigma>0$. Under certain…

We use PDE methods as developed for the Liouville equation to study the existence of conformal metrics with prescribed singularities on surfaces with boundary, the boundary condition being constant geodesic curvature. Our first result shows…

We refine Osserman's argument on the exceptional values of the Gauss map of algebraic minimal surfaces. This gives an effective estimate for the number of exceptional values and the totally ramified value number for a wider class of…

We consider minimising $p$-harmonic maps from three-dimensional domains to the real projective plane, for $1<p<2$. These maps arise as least-energy configurations in variational models for nematic liquid crystals. We show that the singular…

In this paper, we study trigonal minimal surfaces in flat tori. First, we show a topological obstruction similar to that of hyperelliptic minimal surfaces. Actually, the genus of trigonal minimal surface in 3-dimensional flat torus must be…

We prove a general fusion theorem for complete orientable minimal surfaces in $\mathbb{R}^3$ with finite total curvature. As a consequence, complete orientable minimal surfaces of weak finite total curvature with exotic geometry are…

A symmetric quadratic form $g$ on a surface~$M$ is said to be locally Hessianizable if each $p\in M$ has an open neighborhood~$U$ on which there exists a local coordinate chart $(x^1,x^2):U\to\mathbb{R}^2$ and a function $f:U\to\mathbb{R}$…

We survey the recent developments in the theory of quasireg- ular mappings in metric spaces. In particular, we study the geometric porosity of the branch set of quasiregular mappings in general metric measure spaces, and then, introduce the…

In this paper, we study the space of translational limits T(M) of a surface M properly embedded in R^3 with nonzero constant mean curvature and bounded second fundamental form. There is a natural map T which assigns to any surface M' in…

We find all m-spin structures on Klein surfaces of genus larger than one. An m-spin structure on a Riemann surface P is a complex line bundle on P whose m-th tensor power is the cotangent bundle of P. A Klein surface can be described by a…

Let H:(M,p)->(M',p') be a formal mapping between two germs of real-analytic generic submanifolds in C^N with nonvanishing Jacobian. Assuming M to be minimal at p and M' holomorphically nondegenerate at p', we prove the convergence of the…

We give a combinatorial characterization of the group of quasiconformal homeomorphisms of a closed, oriented surface $S$ of genus at least $2$. In particular, we prove they are exactly the automorphisms of a graph of essential quasicircles…

We consider a special case of the outer bi-Lipschitz classification of real semialgebraic (or, more general, definable in a polynomially bounded o-minimal structure) surface germs, obtained as a union of two normally embedded H\"older…

Let (E,D,P) be a flat vector bundle with a parabolic structure over a punctured Riemann surface, (M,g). We consider a deformation of the harmonic metric equation which we call the Poisson metric equation. This equation arises naturally as…

In this paper we study areas (called p-areas) and volumes for parametric surfaces in the 3D-Heisenberg group $\mathbb{H}_1$, which is considered as a flat model of pseudo-hermitian manifolds. We derive the formulas of p-areas and volumes…

If the face\mbox{-}cycles at all the vertices in a map are of same type then the map is called semi\mbox{-}equivelar. A map is called minimal if the number of vertices is minimal. We know the bounds of number of vertex orbits of…

We prove that the composition of a quasi-nearly subharmonic function and a quasiregular mappings of bounded multiplicity is quasi-nearly subharmonic. Also, we prove that if $u\circ f$ is quasi-nearly subharmonic for all quasi-nearly…

We identify the Variational Principle governing inifinity-Harmonic maps, that is solutions to the Infinity-Laplacian. The system was first derived in the limit of the p-Laplacian as p->inifinity in [K2] and is recently studied in [K3]. Here…