Two-dimensional dissipative solitons supported by localized gain.

We show that the balance between localized gain and nonlinear cubic dissipation in the two-dimensional nonlinear Schrödinger equation allows for the existence of stable localized modes that we identify as solitons. Such modes exist only when the gain is strong enough and the energy flow exceeds certain threshold value. Above the critical value of the gain, symmetry breaking occurs and asymmetric dissipative solitons emerge.