We consider codimension 2 sphere congruences in pseudo-conformal geometry that are harmonic with respect to the conformal structure of an orthogonal surface. characterise surfaces such as either $S$-Willmore surfaces, quasi-umbilical constant mean curvature 3-dimensional space forms or lightlike lightcones. then investigate Bryant's quartic differential this context and show generically is dive...

In this paper, we introduce complex functional maps, which extend the map framework to conformal maps between tangent vector fields on surfaces. A key property of these is their orientation awareness. More specifically, demonstrate that unlike regular link spaces two manifolds, our establish a oriented bundles, thus permitting robust and efficient transfer fields. By first endowing then exploit...

Let $(M^4,g)$ be a closed Riemannian manifold of dimension four. We investigate the properties metrics which are critical points eigenvalues Paneitz operator when considered as functionals on space with fixed volume. prove that aforementioned functional restricted to conformal classes associated higher-order analog harmonic maps (known extrinsic conformal-harmonic maps) into round spheres. This...

We prove that all Sierpi\'nski carpets in the plane are non-removable for (quasi)conformal maps. More precisely, we show any two $S,S'\subset \hat{\mathbb{C}}$ there exists a homeomorphism $f\colon \hat{\mathbb{C}}\to is conformal $\hat{\mathbb{C}}\setminus S$ and it maps $S$ onto $S'$. The proof topological utilizes ideas of characterization Whyburn. As corollary, obtain partial answer to ques...

In [Hz], Heinz proved that there is no harmonic diffeomorphism from the unit disk D onto the complex plane C. The result was generalized by Schoen [S] and he proved that there is no harmonic diffeomorphism from the unit disk onto a complete surface of nonnegative curvature. Unlike conformal or quasi-conformal maps between Riemann surfaces, the inverse of a harmonic map is not harmonic in genera...

The main result of this paper proves the existence of multiple solutions to a class of generalized constant mean curvature equations, called H-systems. Also contained is a regularity for conformal nharmonic maps.

We prove that for conformal expanding maps the return time does have constant multifractal spectrum. This is the counterpart of the result by Feng and Wu in the symbolic setting.