In many systems of soft-matter physics or in biology highly confined liquids are of great importance. In these systems the interaction between the boundary of the system and the liquid are relevant and results in an interesting and rich interplay between physics and geometry.
This talk will first address the question of how thermodynamic quantities of highly confined fluids depend on the shape of the confining boundary. The presented connection between geometry and thermodynamics is based on the Hadwiger theorem from integral geometry. These ideas will then be applied to problems of soft and biological matter.