Report
Hodge theory on ALG$^*$ manifolds
| العنوان: | Hodge theory on ALG$^*$ manifolds |
|---|---|
| المؤلفون: | Chen, Gao, Viaclovsky, Jeff, Zhang, Ruobing |
| سنة النشر: | 2021 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Differential Geometry |
| الوصف: | We develop a Fredholm Theory for the Hodge Laplacian in weighted spaces on ALG$^*$ manifolds in dimension four. We then give several applications of this theory. First, we show the existence of harmonic functions with prescribed asymptotics at infinity. A corollary of this is a non-existence result for ALG$^*$ manifolds with non-negative Ricci curvature having group $\Gamma = \{e\}$ at infinity. Next, we prove a Hodge decomposition for the first de Rham cohomology group of an ALG$^*$ manifold. A corollary of this is vanishing of the first betti number for any ALG$^*$ manifold with non-negative Ricci curvature. Another application of our analysis is to determine the optimal order of ALG$^*$ gravitational instantons. Comment: 35 pages; final version; to appear in J. Reine Angew. Math. (Crelle's Journal) |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2109.08782 |
| رقم الانضمام: | edsarx.2109.08782 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |