Isoperimetric Problems in Sectors with Density
نویسندگان
چکیده
We consider the isoperimetric problem in planar sectors with density rp, and with density a > 1 inside the unit disk and 1 outside. We characterize solutions as a function of sector angle. We provide a general symmetrization theorem, and apply it to Rn with radial density.
منابع مشابه
Isoperimetric Problems in Sectors with Density - Report 105 of 7/27
We consider the isoperimetric problem in planar sectors with density rp, and with density a > 1 inside the unit disk and 1 outside. We characterize solutions as a function of sector angle. We provide a very general symmetrization theorem, and apply it to Rn with radial density.
متن کاملRegularity of Isoperimetric Sets in R2 with Density
We consider the isoperimetric problem in R with density for the planar case n = 2. We show that, if the density is C, then the boundary of any isoperimetric is of class C α 3−2α . This improves the previously known regularity.
متن کاملOn the Isoperimetric Problem in Euclidean Space with Density
We study the isoperimetric problem for Euclidean space endowedwith a continuous density. In dimension one, we characterize isoperimetric regions for a unimodal density. In higher dimensions, we prove existence results and we derive stability conditions, which lead to the conjecture that for a radial log-convex density, balls about the origin are isoperimetric regions. Finally, we prove this con...
متن کاملEdge-Isoperimetric Problems for Cartesian Powers of Regular Graphs
We consider an edge-isoperimetric problem (EIP) on the cartesian powers of graphs. One of our objectives is to extend the list of graphs for whose cartesian powers the lexicographic order provides nested solutions for the EIP. We present several new classes of such graphs that include as special cases all presently known graphs with this property. Our new results are applied to derive best poss...
متن کاملIsoperimetric regions in surfaces and in surfaces with density
We study the isoperimetric problem, the least-perimeter way to enclose given area, in various surfaces. For example, in two-dimensional Twisted Chimney space, a twodimensional analog of one of the ten flat, orientable models for the universe, we prove that isoperimetric regions are round discs or strips. In the Gauss plane, defined as the Euclidean plane with Gaussian density, we prove that in ...
متن کامل