论文标题
Dirac操作员的RICCI流下的散射理论和光谱稳定性
Scattering Theory and Spectral Stability under a Ricci Flow for Dirac Operators
论文作者
论文摘要
给定具有固定拓扑结构结构的非合流旋转歧管$ m $，以及$ m $上的两个完整的Riemannian指标$ g $和$ h $，带有有界的部分曲率，我们证明了Wave Operators $ \ MATHSCR {W} {W} _ {w} _ {\ pm}（\ pm} $ and d _ g，d_h，d_g，i g，i g，i g，i g，i g，i g，i g，i g，i g，i g，i g，i g，i g，i g，i g，i g，i g，i g，i g，i g，i g，i g，i g，i g，i g，i g，i g，i_ $ \ mathscr {w} _ {\ pm}（d_h^2，d^2_g，i_ {g，h}）$，其中$ i_ {g，h} $是基础$ l^2 $ space of Spinors的基础上的单位地图。该标准不涉及任何注射性半径假设，并导致标准的标准，即在RICCI流动下，绝对连续光谱及其正方形的稳定性。
Given a noncompact spin manifold $M$ with a fixed topological spin structure and two complete Riemannian metrics $g$ and $h$ on $M$ with bounded sectional curvatures, we prove a criterion for the existence and completeness of the wave operators $\mathscr{W}_{\pm}(D_h, D_g, I_{g,h})$ and $\mathscr{W}_{\pm}(D_h^2, D^2_g, I_{g,h})$, where $I_{g,h}$ is the canonically given unitary map between the underlying $L^2$-spaces of spinors. This criterion does not involve any injectivity radius assumptions and leads to a criterion for the stability of the absolutely continuous spectrum of a Dirac operator and its square under a Ricci flow.
