Unusual comparison properties of capillary surfaces

This talk will address a question that was raised about 30 years ago by Mario Miranda, as to whether a given cylindrical capillary tube always raises liquid higher over its section than does a cylinder whose section strictly contains the given one. Depending on the specific shapes, the answer can take unanticipated forms exhibiting nonuniformity and discontinuous reversal in behavior, even in geometrically simple configurations. The presentation will be for the most part complete and self-contained, and is intended to be accessible for a broad mathematical audience.