تقرير
Comments on the regularity of harmonic maps between singular spaces
| العنوان: | Comments on the regularity of harmonic maps between singular spaces |
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| المؤلفون: | Gennaioli, Luca, Gigli, Nicola, Zhang, Hui-Chun, Zhu, Xi-Ping |
| سنة النشر: | 2024 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Analysis of PDEs, Mathematics - Metric Geometry |
| الوصف: | In this work we are going to establish H\"older continuity of harmonic maps from an open set $\Omega$ in an ${\rm RCD}(K,N)$ space valued into a ${\rm CAT}(\kappa)$ space, with the constraint that the image of $\Omega$ via the map is contained in a sufficiently small ball in the target. Building on top of this regularity and assuming a local Lipschitz regularity of the map, we establish a weak version of the Bochner-Eells-Sampson inequality in such a non-smooth setting. Finally we study the boundary regularity of such maps. Comment: Comments are welcome! |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2408.00479 |
| رقم الأكسشن: | edsarx.2408.00479 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |