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RECTIFIABILITY PROPERTIES OF VARIFOLDS IN l3
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 Title & Authors
RECTIFIABILITY PROPERTIES OF VARIFOLDS IN l3
Zhao, Peibiao; Yang, Xiaoping;
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 Abstract
We prove the following theorem: Given a Varifold V in with the property that 0 < $lim_{r}_{\rightarrow}_{o}\;\frac{{\mu}v(C_{r}(x))}{r^{2}}\;<\;{\infty}\;for\;{\mu}v\;a.e.x\;{\in}$ SptV, then V is rectifiable.
 Keywords
Varifolds;tangent measures;rectifiable sets;rectifiable measures;
 Language
English
 Cited by
1.
INCLUSION AND NEIGHBORHOOD PROPERTIES OF CERTAIN SUBCLASSES OF p-VALENT ANALYTIC FUNCTIONS OF COMPLEX ORDER INVOLVING A LINEAR OPERATOR,;;

대한수학회보, 2014. vol.51. 6, pp.1625-1647 crossref(new window)
 References
1.
W. K. Allard, On the first variation of a varifold, Ann. of Math. (2) 95 (1972), 417-491 crossref(new window)

2.
L. Ambrosio, M. Gobbino, and D. Pallara, Approximation problems for curvature vari-folds, J. Geom. Anal. 8 (1998), no. 1, 1-19 crossref(new window)

3.
L. Ambrosio and B. Kirchheim, Currents in metric spaces, Acta Math. 185 (2000), no. 1, 1-80 crossref(new window)

4.
L. Ambrosio and B. Kirchhei, Rectifiable sets in metric and Banach spaces, Math. Ann. 318 (2000), no. 3, 527-555 crossref(new window)

5.
A. S. Besicovitch, On the fundamental geometrical properties of linearly measurable plane sets of points, Math. Ann. 98 (1928), no. 1, 422-464 crossref(new window)

6.
A. S. Besicovitc, On the fundamental geometrical properties of linearly measurable plane sets of points (II), Math. Ann. 115 (1938), no. 1, 296-329 crossref(new window)

7.
G. David and S. Semmes, Singular integrals and rectifiable sets in $R^n$: Beyond Lipschitz graphs. Ast risque 193, Soc. Math. France, 1991

8.
K. J. Falconer, The geometry of fractal sets, Cambridge Tracts in Mathematics, 85. Cambridge University Press, Cambridge, 1986

9.
H. Federer, The $(\varphi,\kappa)$ rectifiable subsets of n-space, Amer. Math. Soc. 62 (1947), 114-192 crossref(new window)

10.
H. Federer, Geometric measure theory, Die Grundlehren der mathematischen Wissensch-aften, Band 153 Springer-Verlag New York Inc., New York, 1969

11.
F. H. Lin, Varifold type theory for Sobolev mappings, First International Congress of Chinese Mathematicians (Beijing, 1998), 423-430, AMS/IP Stud. Adv. Math., 20, Amer. Math. Soc., Providence, RI, 2001

12.
F. H. Lin and X. P. Yang, Geometric measure theory|an introduction, Advanced Math-ematics (Beijing/Boston), 1. Science Press, Beijing; International Press, Boston, MA, 2002

13.
A. Lorent, Rectifiability of measures with locally uniform cube density, Proc. London. Math. Soc. 86 (2003), no. 1, 153-249 crossref(new window)

14.
A. Lorent, A Marstrand type theorem for measures with cube density in general dimension, Math. Proc. Camb. Phil. Soc. 137 (2004), no. 3, 657-696 crossref(new window)

15.
J. M. Marstrand, Hausdorff two-dimensional measure in 3-space, Proc. London Math. Soc. (3) 11 (1961), 91-108 crossref(new window)

16.
P. Mattila, Hausdorffm regular and rectifiable sets in n-space, Trans. Amer. Math. Soc. 205 (1975), 263-274 crossref(new window)

17.
P. Mattila, Geometry of sets and measures in Euclidean spaces, Fractals and rectifiability. Cambridge Studies in Advanced Mathematics, 44. Cambridge University Press, Cam-bridge, 1995

18.
E. F. Morse, Density ratios and $(\phi,1)$ rectifiability in n-space, Trans. Amer. Math. Soc. 69 (1950), 324-334 crossref(new window)

19.
P. Morters and D. Preiss, Tangent measure distributions of fractal measures, Math. Ann. 312 (1998), no. 1, 53-93 crossref(new window)

20.
T. D. Pauw, Nearly flat almost monotone measures are big pieces of Lipschitz graphs, J. Geom. Anal. 12 (2002), no. 1, 29-61 crossref(new window)

21.
D. Preiss, Geometry of measures in $R^n$: distribution, rectifiability, and densities, Ann. of Math. (2) 125 (1987), no. 3, 537-643 crossref(new window)

22.
I. Rubinstein and L. Rubinstein, Partial Differential Equations in Classical Mathenatical Physics, Cambridge University Press, 1998

23.
L. Simon, Lectures on geometric measure theory, Proceedings of the Centre for Math-ematical Analysis, Australian National University, 3. Australian National University, Centre for Mathematical Analysis, Canberra, 1983

24.
P. B. Zhao and X. P. Yang, Some remarks on currents in metric spaces, Southeast Asian Bulletin of Mathematics, 29 (2005), no. 5, 1011-1021

25.
P. B. Zhao and X. P. Yang, Geometric Analysis of Tangent Merasures, Chinese Annals of mathematics 26 (2005), no. 2, 151-164

26.
P. B. Zhao and X. P. Yang, Marstrand Theorem for Cube in $R^d$ with respect to Varifolds, in preparation