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We stabilize nematic droplets with handles against surface-tension-driveninstabilities using a yield-stress material as outer fluid and study thecomplex nematic textures and defect structures that result from the competitionbetween topological constraints and the elasticity of the nematic liquidcrystal. We uncover a surprisingly persistent twisted configuration of thenematic director inside the droplets when tangential anchoring is establishedat their boundaries, which we explain after considering the influence ofsaddle-splay on the elastic free energy. For toroidal droplets, we find thatthe saddle-splay energy screens the twisting energy resulting in a spontaneousbreaking of mirror symmetry; the chiral twisted state persists for aspectratios as large as ~20. For droplets with additional handles, we observe inexperiments and computer simulations that there are two additional -1 surfacedefects per handle; these are located in regions with local saddle geometry tominimize the nematic distortions and hence the corresponding elastic freeenergy.

Stable nematic droplets with handles