体谱的一个次可加不等式
A sub-additive inequality for the volume spectrum
摘要：
设$(M,g)$是闭黎曼流形，$\{ω_p\}_{p=1}^{\infty}$是$(M,g)$的体谱.我们将证明对于所有$k,m\geq 0$的$ω_{k+m+1}\leq ω_k+ω_m+W$，其中$ω_0=0$和$W$是$(M,g)$的单参数Almart-Pitts宽度。我们也将使用Allen-Cahn方法证明$\varepsilon$ -相变谱$\{c_{\varepsilon}(p)\}_{p=1}^{\infty}$的类似不等式。
英文摘要：
Let $(M,g)$ be a closed Riemannian manifold and $\{ω_p\}_{p=1}^{\infty}$ be the volume spectrum of $(M,g)$. We will show that $ω_{k+m+1}\leq ω_k+ω_m+W$ for all $k,m\geq 0$, where $ω_0=0$ and $W$ is the one-parameter Almgren-Pitts width of $(M,g)$. We will also prove the similar inequality for the $\varepsilon$-phase-transition spectrum $\{c_{\varepsilon}(p)\}_{p=1}^{\infty}$ using the Allen-Cahn approach.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
