We have studied the dynamics of monolayer Au islands on a Au(100) electrode in sulfuric acid using electrochemical scanning tunneling microscopy. We present quantitative studies of the equilibrium shape of Au islands on Au(100) electrodes and of the thermal fluctuations around the equilibrium shape. As was recently demonstrated for islands on metal surfaces under ultra-high vacuum, step and kink energies may be determined. Furthermore, we present data on the decay of Au islands on Au(100) electrodes due to Ostwald ripening and due to the reformation of the potential-induced reconstruction on the gold electrode. In both cases we observe that different dominant mass transport processes control the island decay. In the case of island decay during potential-induced reformation of the reconstruction, we find furthermore evidence for rapid island decay processes as were recently reported for metal surfaces in ultra-high vacuum studies.