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Improved local energy decay for the wave equation on asymptotically Euclidean odd dimensional manifolds in the short range case
Local energy decay resolvent smoothness wave equation odd dimensions low frequencies asymptotically Euclidean manifolds
2011/9/21
Abstract: We show improved local energy decay for the wave equation on asymptotically Euclidean manifolds in odd dimensions in the short range case. The precise decay rate depends on the decay of the ...
Do absolutely irreducible group actions have odd dimensional fixed point spaces?
odd dimensional fixed point
2010/11/23
In his volume [5] on "Symmetry Breaking for Compact Lie Groups" Mike Field quotes a private communication by Jorge Ize claiming that any bifurcation problem with absolutely irreducible group action wo...
Uniqueness on the Class of Odd-Dimensional Starlike Obstacles with Cross Section Data
Odd-Dimensional Starlike Obstacles Cross Section Data
2010/11/18
We determine the uniqueness on starlike obstacles by using the cross section data. We see cross section data as spectral measure in polar coordinate at far field. Cross section scattering data suffic...
The Connes-Chern Character and The Atiyah-Patodi-Singer Index Theorem for Odd Dimensional Manifolds with Boundary
The Connes-Chern Character The Atiyah-Patodi-Singer Index Theorem
2010/11/9
We prove an analogue for odd dimensional manifolds with boundary, in the $b$-calculus setting, of the higher Atiyah-Patodi-Singer index theorem by Getzler and by Wu.