اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدAstalas Conjecture on Distortion of Hausdorff Measures under Quasiconformal Maps in the Plane
124
0
0.0
(
0
)
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
Let E be a compact set in the plane, g be a K-quasiconformal map, and let 0<t<2. Then H^t (E) = 0 implies H^{t} (g E) = 0, for t=[2Kt]/[2+(K-1)t]. This is a refinement of a set of inequalities on the distortion of Hausdorff dimensions by quasiconformal maps proved by K. Astala in his celebrated paper on area distortion for quasiconformal maps and answers in the positive a Conjecture of K. Astala in op. cit.
قيم البحث
اقرأ أيضاً
Suppose that $E$ and $E$ denote real Banach spaces with dimension at least $2$ and that $Dsubset E$ and $Dsubset E$ are domains. In this paper, we establish, in terms of the $j_D$ metric, a necessary and sufficient condition for the homeomorphism $f:
E to E$ to be FQC. Moreover, we give, in terms of the $j_D$ metric, a sufficient condition for the homeomorphism $f: Dto D$ to be FQC. On the other hand, we show that this condition is not necessary.
We consider the variational problem consisting of minimizing a polyconvex integrand for maps between manifolds. We offer a simple and direct proof of the existence of a minimizing map. The proof is based on Young measures.
By using the method of Loewner chains, we establish some sufficient conditions for the analyticity and univalency of functions defined by an integral operator. Also, we refine the result to a quasiconformal extension criterion with the help of Beckerss method.
In the present paper, we obtain a more general conditions for univalence of analytic functions in the open unit disk U. Also, we obtain a refinement to a quasiconformal extension criterion of the main result.
We investigate a variant of the Beurling-Ahlfors extension of quasisymmetric homeomorphisms of the real line that is given by the convolution of the heat kernel, and prove that the complex dilatation of such a quasiconformal extension of a strongly s
ymmetric homeomorphism (i.e. its derivative is an ${rm A}_infty$-weight whose logarithm is in VMO) induces a vanishing Carleson measure on the upper half-plane.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
