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Curvature bounds of Euclidean cones of spheres
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Abstract
In this paper, we obtain the optimal condition of the curvaturebounds guaranteeing that Euclidean cones over Aleksandrov spacesof curvature bounded above preserve the curvature bounds, byconsidering the Euclidean cone CS^n_r over n-dimensionalsphere S^n_r of radius r. More precisely, we show that for r<1, the Euclidean cone CS^n_r of S^n_r is a CBB(0) space, butnot a CBA(kappa)-space for any real kappa in R.
관련 논문AI추천
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