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A Support Characterization for Functions Defined on $\Bbb S^{n}$ with Vanishing Integrals on Subspheres Arising from Axially Symmetric Surfaces. (arXiv:1810.06614v1 [math.AP])
来源于:arXiv
Let $\Sigma$ be a closed, smooth hypersurface in $\Bbb R^{n + 1}$ which is
axially symmetric and is contained inside the unit sphere $\Bbb S^{n}$. For a
continuous function $f$, which is defined on $\Bbb S^{n}$, the main goal of
this paper is to characterize the support of $f$ in case where its integrals
vanish on subspheres obtained by intersecting $\Bbb S^{n}$ with the tangent
hyperplanes of a certain subdomain $\mathcal{U}\subset\Sigma$ of $\Sigma$. We
show that the support of $f$ can be characterized in case where its integrals
also vanish on subspheres obtained by intersecting $\Bbb S^{n}$ with
hyperplanes obtained by infinitesimal perturbations of the tangent hyperplanes
of $\mathcal{U}$. 查看全文>>