arXiv subjects

Zahra Sinaei

Publications and source records attributed to Zahra Sinaei.

4 recordsLinked to original sources

arXiv2017

Convex functional and the stratification of the singular set of their stationary points

We prove partial regularity of stationary solutions and minimizers $u$ from a set $Ω\subset \mathbb R^n$ to a Riemannian manifold $N$, for the functional $\int_ΩF(x,u,|\nabla u|^2) dx$. The integrand $F$ is convex and satisfies some ellipticity and boundedness assumptions. We also develop a new monotonicity formula and an $ε$-regularity theorem for such stationary solutions with no restriction on their images. We then use the idea of quantitative stratification to show that the k-th strata of the singular set of such solutions are k-rectifiable.

math.DG↗

arXiv2014

Riemannian Polyhedra and Liouville-type Theorems for Harmonic maps

This paper is a study of harmonic maps from Riemannian polyhedra to (locally) non-positively curved geodesic spaces in the sense of Alexandrov. We prove Liouville-type theorems for subharmonic functions and harmonic maps under two different assumptions on the source space. First we prove the analogue of the Schoen-Yau Theorem on a complete (smooth) pseudomanifolds with non-negative Ricci curvature. Then we study 2-parabolic admissible Riemannian polyhedra and prove some vanishing results on them.

math.MG↗

arXiv2014

Convergence of harmonic maps

In this paper we prove a compactness theorem for a sequence of harmonic maps which are defined on a converging sequence of Riemannian manifolds.

math.DG↗

arXiv2014

Intrinsic Flat Convergence of Covering Spaces

We examine the limits of covering spaces and the covering spectra of oriented Riemannian manifolds, $M_j$, which converge to a nonzero integral current space, $M_\infty$, in the intrinsic flat sense. We provide examples demonstrating that the covering spaces and covering spectra need not converge in this setting. In fact we provide a sequence of simply connected $M_j$ diffeomorphic to $\mathbb{S}^4$ that converge in the intrinsic flat sense to a torus $\mathbb{S}^1\times\mathbb{S}^3$. Nevertheless, we prove that if the $δ$-covers, $\tilde{M}_j^δ$, have finite order $N$, then a subsequence of the $\tilde{M}_j^δ$ converge in the intrinsic flat sense to a metric space, $M^δ_\infty$, which is the disjoint union of covering spaces of $M_\infty$.

math.MG↗