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Introduction x - math.ucla.edu
KIRSZBRAUN-TYPE THEOREMS FOR GRAPHSNISHANT CHANDGOTIA, IGOR PAK, AND MARTIN classicalKirszbraun theoremsays that all 1-Lipschitz functionsf:A Rn,A Rn, with the Euclidean metric have a 1-Lipschitz extension toRn. For metric spacesX,Ywesay thatYisX-Kirszbraunif all 1-Lipschitz functionsf:A Y,A X, have a 1-Lipschitzextension toX. We analyze the case whenXandYare graphs with the usual path metric. Weprove thatZd-Kirszbraun graphs are exactly graphs that satisfies a certainHelly s property. Wealso consider complexity aspects of these results in metric geometry is important for many applications, ranging from discretedifferential geometry to numerical methods.
KIRSZBRAUN-TYPE THEOREMS FOR GRAPHS NISHANT CHANDGOTIA, IGOR PAK, AND MARTIN TASSY Abstract. The classical Kirszbraun theorem says that all 1-Lipschitz functions f : A!
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