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Lytchak, Alexander; Stadler, Stephan (2020): IMPROVEMENTS OF UPPER CURVATURE BOUNDS. In: Transactions of the American Mathematical Society, Vol. 373, No. 10: pp. 7153-7166
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We prove that upper curvature bounds in the sense of Alexandrov can be improved locally by using appropriate conformal changes. As a new technical tool we derive a generalization to metric spaces and semi-convex functions of the classical differential geometric property that compositions of harmonic maps with convex functions are subharmonic.