论文标题
低维riemannian产品中的等量估计值
Isoperimetric estimates in low dimensional Riemannian products
论文作者
论文摘要
令$（t^k，h_k）=（s_ {r_1}^1 \ times S_ {r_2}^1 \ times ... $（\ Mathbb r^n，g_e）$带有平坦度量的欧几里得空间。我们计算$（T^2 \ times \ Mathbb r^n，h_2+g_e）$，$ 2 \ leq n \ leq 5 $的等级概要概要文件。这些计算给出了$ t^2 \ times \ mathbb r^n $的等级配置文件的明确下限。我们还注意到，可以计算$（T^K \ Times \ Mathbb r^n，h_k+g_e）$，$ 2 \ leq k \ leq5 $，$ 2 \ leq n \ leq 7-k $，可以计算，提供$（T^{k-1} \ times \ mathbb r^n $ 1} $（n Nem）我们以$ k = 3 $的方式明确计算了此。我们根据A. Ros和F. Morgan的工作使用对称技术对产品歧管。
Let $(T^k,h_k)=(S_{r_1}^1\times S_{r_2}^1 \times ... \times S_{r_k}^1, dt_1^2+dt_2^2+...+dt_k^2)$ be flat tori, $r_k\geq ...\geq r_2\geq r_1>0$ and $(\mathbb R^n,g_E)$ the Euclidean space with the flat metric. We compute the isoperimetric profile of $(T^2\times \mathbb R^n, h_2+g_E)$, $2\leq n\leq 5$, for small and big values of the volume. These computations give explicit lower bounds for the isoperimetric profile of $T^2\times\mathbb R^n$. We also note that similar estimates for $(T^k\times \mathbb R^n, h_k+g_E)$, $2\leq k\leq5$, $2\leq n\leq 7-k$, may be computed, provided estimates for $(T^{k-1}\times \mathbb R^{n+1}, h_{k-1}+g_E)$ exist. We compute this explicitly for $k=3$. We use symmetrization techniques for product manifolds, based on work of A. Ros and F. Morgan.
