Density estimates for compact surfaces with total boundary curvature   less than 4pi
  In this paper we obtain density estimates for compact surfaces immersed in R^n with total boundary curvature less than 4pi and with sufficiently small L^p norm of the mean curvature, p>2. Our results generalize the main results in [2]. We then apply our estimates to discuss the geometry and topology of such surfaces. 
Theodora Bourni, Giuseppe Tinaglia
math.DG