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Dirac Operators with $W^{1,\infty}$-potential under Codimension one Collapse. (arXiv:1707.00608v1 [math.SP])

来源于:arXiv
We study the behavior of the spectrum of the Dirac operator together with a symmetric $W^{1, \infty}$-potential on spin manifolds under a collapse of codimension one with bounded sectional curvature and diameter. If there is an induced spin structure on the limit space $N$ then there are convergent eigenvalues which converge to the spectrum of a first order differential operator $D$ on $N$ together with a symmetric $W^{1,\infty}$-potential. If the dimension of the limit space is even then $D$ is the Dirac operator $D^N$ on $N$ and if the dimension of the limit space is odd, then $D = D^N \oplus -D^N$. 查看全文>>