تقرير
Harmonic projections in negative curvature
| العنوان: | Harmonic projections in negative curvature |
|---|---|
| المؤلفون: | Tošić, Ognjen |
| سنة النشر: | 2022 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Differential Geometry, 53C43 |
| الوصف: | In this paper we construct harmonic maps that are at a bounded distance from nearest-point retractions to convex sets, in negatively curved manifolds. Specifically, given a quasidisk $Q$ in hyperbolic space, we construct a harmonic map to the hyperbolic plane that corresponds to the nearest-point retraction to the convex hull of $Q$. If $M$ is a pinched Hadamard manifold so that its isometry group acts with cobounded orbits, and if $S$ is a set in the boundary at infinity of $M$, with the property that all elements of its orbit under the isometry group of $M$ have dimension less than $\frac{n-1}{2}$, we show that the nearest-point retraction to the convex hull of $S$ is a bounded distance away from some harmonic map. Comment: 26 pages, 0 figures |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2203.02578 |
| رقم الأكسشن: | edsarx.2203.02578 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |