  We study the surface transport properties of stationary localized
configurations of relativistic fluids to the first two non-trivial orders in a
derivative expansion. By demanding that these finite lumps of relativistic
fluid are described by a thermal partition function with arbitrary stationary
background metric and gauge fields, we are able to find several constraints
among surface transport coefficients. At leading order, besides recovering the
surface thermodynamics, we obtain a generalization of the Young-Laplace
equation for relativistic fluid surfaces, by considering a temperature
dependence in the surface tension, which is further generalized in the context
of superfluids. At the next order, for uncharged fluids in 3+1 dimensions, we
show that besides the 3 independent bulk transport coefficients previously
known, a generic localized configuration is characterized by 3 additional
surface transport coefficients, one of which may be identified with the surface
modulus of rigidity. Finally, as an application, we study the effect of
temperature dependence of surface tension on some explicit examples of
localized fluid configurations, which are dual to certain non-trivial black
hole solutions via the AdS/CFT correspondence.

High Energy Physics - Theory;Soft Condensed Matter