AbstractsMathematics

In this thesis, a self-contained proof is given of the regularity of minimal surfaces via viscosity solutions, following the ideas of L.Caffarelli,X.Cabré [2], O.Savin[11][12], E.Giusti[7] and J.Roquejoffre[8], where we expand upon the ideas and give full details on the approach. Basically the proof of the program consists of four parts: 1) Density and measure estimates, 2) Viscosity solution methods of elliptic equations , 3) a geometric Harnack inequality and 4) iteration of the De Giorgi flatness result.