# Stationary measures and rectifiability

## Related Articles

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For a locally compact groupoid G with a fixed Haar system Î» and quasi-invariant measure Âµ, we introduce the notion of Î»-measurability and construct the space LÂ¹(G, Î», Âµ) of absolutely integrable functions on G and show that it is a Banach *-algebra and a two-sided ideal in the...

- A supplement to ‘A note on invariant measure semigroups’. Tserpes, N. // Semigroup Forum;Sep/Oct2009, Vol. 79 Issue 2, p417
A unified definition of measure semigroup is given and it is shown how the types of invariance for the measure are formulated and what effect they have on the embeddability of an Abelian semigroup in a group.

- NON-REGULAR TANGENTIAL BEHAVIOUR OF A MONOTONE MEASURE. JAN KOLÁŘ // Bulletin of the London Mathematical Society;Aug2006, Vol. 38 Issue 4, p657
A Radon measure $\mu$ on ${mathbb R}^n$ is said to be $k$-monotone if $r\mapsto{\mu(B(x,r))}/{r^k}$ is a non-decreasing function on $(0,\infty)$ for every $x\in {\mathbb R}^n$. (If $\mu$ is the $k$-dimensional Hausdorff measure restricted to a $k$-dimensional minimal surface then this important...

- EXISTENCE OF SOLUTIONS FOR SOME NONLINEAR ELLIPTIC EQUATIONS. Anane, Aomar; Chakrone, Omar; Chehabi, Mohammed // Electronic Journal of Differential Equations;2006, Vol. 2006, Special section p1
In this paper, we study the existence of solutions to the following nonlinear elliptic problem in a bounded subset Î© of â„N: -&Deltap u = f (x, u, â–½u) + Î¼ in Î©, u = 0 on âˆ‚Î©, where Î¼ is a Radon measure on Î© which is zero on sets of p-capacity zero, f: Î© x...

- On the minimality of the p -harmonic map for weighted energy. Jean-Christophe Bourgoin // Annals of Global Analysis & Geometry;Aug2007, Vol. 32 Issue 1, p1
AbstractÂ Â In this paper, we study the minimality of the map $$\frac{x}{\|x\|}$$ for the weighted energy functional $$E_{f,p}= \int_{\mathbf{B}^n}f(r)\|\nabla u\|^p dx$$, where $$f : [0,1] \rightarrow \mathbb{R}^{}$$ is a continuous function. We prove that for any integer $$p \in \{2,...

- A Note on KÃ¤hlerâ€“Ricci Soliton. Xiuxiong Chen; Song Sun; Gang Tian // IMRN: International Mathematics Research Notices;Sep2009, Vol. 2009 Issue 17, p3328
The article presents a proof of theorem on KÃ¤hler-Ricci soliton, which is not based on the previous equations of Frankel conjecture. It outlines theorem on n-dimensional compact complex manifold and compact KÃ¤hler manifold with positive bisectional curvature. Remarks on the use of Frankel...

- SINGULAR DRESSING ACTIONS ON HARMONIC MAPS. CORREIA, N.; PACHECO, R. // Quarterly Journal of Mathematics;Mar2011, Vol. 62 Issue 1, p71
In this paper we prove that any harmonic map Ï† from a two-sphere S2 into an arbitrary compact semisimple matrix Lie group G may be reduced to a constant by using the singular dressing actions introduced in (M. J. Bergvelt and M. A. Guest, Action of loop groups on harmonic maps, Trans. Amer....

- The Blow-up Locus of Heat Flows for Harmonic Maps. Li, Jiayu; Tian, Gang // Acta Mathematica Sinica;2000, Vol. 16 Issue 1, p29
Abstract Let M and N be two compact Riemannian manifolds. Let u[sub k](x, t) be a sequence of strong stationary weak heat flows from M x R[sup +] to N with bounded energies, Assume that u[sub k] arrow right u weakly in II[sup 1'2](M x R[sup +], N) and that SIGMA[sup +] is the blow-up set for a...

- On harmonic maps from R[sup 1,1] into Hilbert loop groups. Qing Ding; Bao-Qun Lu // Journal of Mathematical Physics;Aug96, Vol. 37 Issue 8, p4076
Atudies the harmonic maps from the Minkowski plane R[sup1.1] into Hilbert loop groups. Calculation of the structure constants of the Hilbert loop groups; Geometric properties of loop groups; Existence of the Cauchy problem for harmonic maps from R[sup 1.1] into certain Hilbert loop groups.