Minkowski content and local Minkowski content for a class of self-conformal sets
نویسندگان
چکیده
منابع مشابه
Minkowski Content for Reachable Sets
In 1955, Martin Kneser showed that the Minkowski content of a compact p-rectifiable subset M of Rn is equal to its p-Hausdorff measure: lim t→0,t>0 Ln ` B(M, t) ́ α(n− p) tn−p = H(M). We extend his result to the reachable sets of a linear control system
متن کاملThe Minkowski and conformal superspaces
We define complex Minkowski superspace in 4 dimensions as the big cell inside a complex flag supermanifold. The complex conformal supergroup acts naturally on this super flag, allowing us to interpret it as the conformal compactification of complex Minkowski superspace. We then consider real Minkowski superspace as a suitable real form of the complex version. Our methods are group theoretic, ba...
متن کاملOne-sided Minkowski content for some classes of closed sets and applications to stochastic geometry
We find conditions ensuring the existence of the one-sided Minkowski content for d-dimensional closed sets in R, in connection with regularity properties of their boundaries. Moreover, we provide a class of sets stable under finite unions for which the one-sided Minkowski content exists. It follows, in particular, that finite unions of sets with Lipschitz boundary and a type of sets with positi...
متن کاملMinkowski Geometric Algebra of Complex Sets
A geometric algebra of point sets in the complex plane is proposed, based on two fundamental operations: Minkowski sums and products. Although the (vector) Minkowski sum is widely known, the Minkowski product of two-dimensional sets (induced by the multiplication rule for complex numbers) has not previously attracted much attention. Many interesting applications, interpretations, and connection...
متن کاملGeneral Minkowski type and related inequalities for seminormed fuzzy integrals
Minkowski type inequalities for the seminormed fuzzy integrals on abstract spaces are studied in a rather general form. Also related inequalities to Minkowski type inequality for the seminormed fuzzy integrals on abstract spaces are studied. Several examples are given to illustrate the validity of theorems. Some results on Chebyshev and Minkowski type inequalities are obtained.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Geometriae Dedicata
سال: 2011
ISSN: 0046-5755,1572-9168
DOI: 10.1007/s10711-011-9661-5