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51
ISOPERIMETRIC REGIONS IN CONES
, 2002
"... We consider cones C = 0 × M n and prove that if the Ricci curvature of C is nonnegative, then geodesic balls about the vertex minimize perimeter for given volume. If strict inequality holds, then they are the only stable regions. ..."
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Cited by 6 (1 self)
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We consider cones C = 0 × M n and prove that if the Ricci curvature of C is nonnegative, then geodesic balls about the vertex minimize perimeter for given volume. If strict inequality holds, then they are the only stable regions.
Isoperimetric Regions in Gauss Sectors
, 2007
"... We consider the free boundary isoperimetric problem in sectors of the Gauss plane. The solution is not always a circular arc as in sectors of the Euclidean plane. We prove that the solution is sometimes a ray and we conjecture that the solution is sometimes a ”rounded ngon ” which we discovered com ..."
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We consider the free boundary isoperimetric problem in sectors of the Gauss plane. The solution is not always a circular arc as in sectors of the Euclidean plane. We prove that the solution is sometimes a ray and we conjecture that the solution is sometimes a ”rounded ngon ” which we discovered
Isoperimetric regions in surfaces and in surfaces with density
, 2006
"... We study the isoperimetric problem, the leastperimeter way to enclose given area, in various surfaces. For example, in twodimensional 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 st ..."
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Cited by 1 (0 self)
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We study the isoperimetric problem, the leastperimeter way to enclose given area, in various surfaces. For example, in twodimensional 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
ISOPERIMETRIC REGIONS IN A WEIGHTED 2DIMENSIONAL LATTICE
"... To my mother Abstract. We investigate isoperimetric regions in the 1 st quadrant of the 2 dimensional lattice, where each point is weighted by the sum of its coordinates. We analyze the isoperimetric properties of six types of regions located in the …rst quadrant of the Cartesian plane: squares, rec ..."
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To my mother Abstract. We investigate isoperimetric regions in the 1 st quadrant of the 2 dimensional lattice, where each point is weighted by the sum of its coordinates. We analyze the isoperimetric properties of six types of regions located in the …rst quadrant of the Cartesian plane: squares
LARGE ISOPERIMETRIC REGIONS IN ASYMPTOTICALLY HYPERBOLIC MANIFOLDS
, 2014
"... We show the existence of isoperimetric regions of sufficiently large volumes in general asymptotically hyperbolic three manifolds. Furthermore, we show that large coordinate spheres in compact perturbations of SchwarzschildantideSitter are uniquely isoperimetric. This is relevant in the context o ..."
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We show the existence of isoperimetric regions of sufficiently large volumes in general asymptotically hyperbolic three manifolds. Furthermore, we show that large coordinate spheres in compact perturbations of SchwarzschildantideSitter are uniquely isoperimetric. This is relevant in the context
Isoperimetric regions in the plane with density r^p
, 2010
"... We consider the isoperimetric problem in the plane with density r p, p> 0, and prove that the solution is a circle through the origin. We use the stability of this isoperimetric curve to prove an ..."
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Cited by 12 (0 self)
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We consider the isoperimetric problem in the plane with density r p, p> 0, and prove that the solution is a circle through the origin. We use the stability of this isoperimetric curve to prove an
Isoperimetric regions in rotationally symmetric convex bodies
"... ABSTRACT. We consider the isoperimetric problem of minimizing perimeter for given volume in a strictly convex domain Ω ⊂ R n+1 and prove that, if Ω is rotationally symmetric about some line, then any solution to this problem must be convex. 1. ..."
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Cited by 3 (1 self)
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ABSTRACT. We consider the isoperimetric problem of minimizing perimeter for given volume in a strictly convex domain Ω ⊂ R n+1 and prove that, if Ω is rotationally symmetric about some line, then any solution to this problem must be convex. 1.
ISOPERIMETRIC REGIONS IN SPHERICAL CONES AND YAMABE CONSTANTS OF M × S¹
, 2007
"... We study isoperimetric regions on Riemannian manifolds of the form (M n × (0, π), sin²(t)g + dt²) where g is a metric of positive Ricci curvature ≥ n − 1. When g is an Einstein metric we use this to compute the Yamabe constant of (M × R, g+dt²) and so to obtain lower bounds for the Yamabe invariant ..."
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Cited by 5 (0 self)
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We study isoperimetric regions on Riemannian manifolds of the form (M n × (0, π), sin²(t)g + dt²) where g is a metric of positive Ricci curvature ≥ n − 1. When g is an Einstein metric we use this to compute the Yamabe constant of (M × R, g+dt²) and so to obtain lower bounds for the Yamabe
STABLE AND ISOPERIMETRIC REGIONS IN ROTATIONALLY SYMMETRIC TORI WITH DECREASING GAUSS CURVATURE
, 2006
"... Abstract. In this work we classify the stable regions (second order minima of perimeter under an area constraint) in tori of revolution with piecewise continuous decreasing Gauss curvature from the longest parallel and with a horizontal symmetry. Some applications to isoperimetric problems are also ..."
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Abstract. In this work we classify the stable regions (second order minima of perimeter under an area constraint) in tori of revolution with piecewise continuous decreasing Gauss curvature from the longest parallel and with a horizontal symmetry. Some applications to isoperimetric problems are also
Results 1  10
of
51