Density Estimates for Compact Surfaces with Total Boundary Curvature Less Than 4 pi

作者：Bourni Theodora; Tinaglia Giuseppe^*

来源：Communications in Partial Differential Equations, 2012, 37(10): 1870-1886.

DOI：10.1080/03605302.2012.686550

• Density estimates
• Embeddedness
• Mean curvature
• Monotonicity formula

In this paper we obtain density estimates for compact surfaces immersed in R-n with total boundary curvature less than 4 pi and with sufficiently small L-p norm of the mean curvature, p %26gt;= 2. In fact we show that these estimates hold for compact branched immersions. Our results generalize the main results in [2]. We then apply our estimates to discuss the geometry and topology of such surfaces.

• 出版日期2012