The size and shape of equilibrium capillary surfaces

The classical theory of capillary is concerned largely with size and shape estimates in symmetric asymptotic configurations. Recent developments leading to global results for all symmetric cases, and to qualitative information on asymptotic properties are discussed. Additional stability criteria are described. Asymmetric situations leading to behavior that differs strikingly from the symmetric case are discussed. When gravity vanishes, capillary surfaces in the accustomed sense may not appear. The question of characterizing those tubes in which surfaces can be found has partially been settled. Progress toward determining the effects of contact angle hysteresis in cases of particular interest is reported.