It is well known that every smooth surface S is at least locally generated by the Dirac equation with real potential. In this dissertation, we study the inverse problem of recovering this potential and surface based on given Gaussian curvature and discrete Cauchy data on assuming that S is a Willmore surface We reduce this problem to several problems of the type:

with given discrete Cauchy data on {} For sequence we assume Blaschke condition

Our main tool is Carleman estimates.