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

TY - JOUR

T1 - Density Estimates for Compact Surfaces with Total Boundary Curvature Less Than 4π

AU - Bourni, Theodora

AU - Tinaglia, Giuseppe

PY - 2012/10

Y1 - 2012/10

N2 - 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 >= 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.

AB - 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 >= 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.

U2 - 10.1080/03605302.2012.686550

DO - 10.1080/03605302.2012.686550

M3 - Article

SN - 0360-5302

VL - 37

SP - 1870

EP - 1886

JO - COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS

JF - COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS

IS - 10

ER -