Difference between revisions of "User:Luca.Spolaor/sandbox"
From Encyclopedia of Mathematics
Luca.Spolaor (talk | contribs) |
Luca.Spolaor (talk | contribs) |
||
| Line 9: | Line 9: | ||
'''Definition 1''' | '''Definition 1''' | ||
| − | Let $m\leq n$. | + | Let $m\leq n$. A m-[[Rectifiable varifold]] is a couple $(M, \theta)$, where $M$ is a m-dimensional [[Rectifiable set]] in $\mathbb R^n$ and $\theta$ is a $\mathcal H^m$ measurable function defined on $M$, called the density function. A varifold is calle integral rectifiable if $\theta$ is integer valued. |
Revision as of 09:53, 11 September 2012
2020 Mathematics Subject Classification: Primary: 49Q15 [MSN][ZBL]
Rectifiable varifolds are a generalization of rectifiable sets in the sense that they allow for a density function to be defined on the set. They are also strictly connected to rectifiable currents, in fact to such a current one can always associate a varifold by putting aside the orientation.
Definitions
Definition 1 Let $m\leq n$. A m-Rectifiable varifold is a couple $(M, \theta)$, where $M$ is a m-dimensional Rectifiable set in $\mathbb R^n$ and $\theta$ is a $\mathcal H^m$ measurable function defined on $M$, called the density function. A varifold is calle integral rectifiable if $\theta$ is integer valued.
First Variation and Stationariety
Allard's Regularity Theorem
References
| [Sim] | Leon Simon, "Lectures on Geometric Measure Theory". Proceedings of the centre for Mathematical Analysis. Australian National University, Canberra, 1983. MR0756417Zbl 0546.49019 |
| [FX] | Lin Fanghua, Yang Xiaoping, "Geometric Measure Theory-An Introduction". Advanced Mathematics Vol.1. International Press, Boston, 2002. MR2030862Zbl 1074.49011 |
How to Cite This Entry:
Luca.Spolaor/sandbox. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Luca.Spolaor/sandbox&oldid=27889
Luca.Spolaor/sandbox. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Luca.Spolaor/sandbox&oldid=27889