论文标题
体积频谱的亚加addive不平等
A sub-additive inequality for the volume spectrum
论文作者
论文摘要
令$（m，g）$为封闭的riemannian歧管，$ \ {ω_p\} _ {p = 1}^{\ infty} $是$（m，g）$的音量频谱。我们将证明$ω_{k+m+1} \ leqω_k+ω_m+w $对于所有$ k，m \ geq 0 $，其中$ω_0= 0 $ and $ w $是单参数almgren-pitts $（m，g）$的单参数almgren-pitts。我们还将证明$ \ varepsilon $ -phase-transition spectrum $ \ {c _ {\ varepsilon}（p）\} _ {p = 1}^{\ infty} $使用Allen-cahn方法。
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.
