Isometries of intrinsic metrics on strictly convex domains

1987 ◽  
Vol 196 (3) ◽  
pp. 343-353 ◽  
Author(s):  
Kam-Wing Leung ◽  
Giorgio Patrizio ◽  
Pit-Mann Wong
Keyword(s):  
Convex Domains ◽  
Intrinsic Metrics ◽  
Strictly Convex

Hilbert Geometry for Strictly Convex Domains

2004 ◽  
Vol 105 (1) ◽  
pp. 29-42 ◽  
Author(s):  
Bruno Colbois ◽  
Patrick Verovic
Keyword(s):  
Convex Domains ◽  
Hilbert Geometry ◽  
Strictly Convex

Saturated systems of symmetric convex domains; results of Eggleston, Bambah and Woods

1973 ◽  
Vol 74 (1) ◽  
pp. 107-116 ◽  
Author(s):  
Vishwa Chander Dumir ◽  
Dharam Singh Khassa
Keyword(s):  
Lower Bound ◽  
Lebesgue Measure ◽  
Convex Domain ◽  
Gauge Function ◽  
Symmetric Convex ◽  
Convex Domains ◽  
Strictly Convex ◽  
Point Set ◽  
Image Position

Let K be a closed, bounded, symmetric convex domain with centre at the origin O and gauge function F(x). By a homothetic translate of K with centre a and radius r we mean the set {x: F(x−a) ≤ r}. A family ℳ of homothetic translates of K is called a saturated family or a saturated system if (i) the infimum r of the radii of sets in ℳ is positive and (ii) every homothetic translate of K of radius r intersects some member of ℳ. For a saturated family ℳ of homothetic translates of K, let S denote the point-set union of the interiors of members of ℳ and S(l), the set S ∪ {x: F(x) ≤ l}. The lower density ρℳ(K) of the saturated system ℳ is defined bywhere V(S(l)) denotes the Lebesgue measure of the set S(l). The problem is to find the greatest lower bound ρK of ρℳ(K) over all saturated systems ℳ of homothetic translates of K. In case K is a circle, Fejes Tóth(9) conjectured thatwhere ϑ(K) denotes the density of the thinnest coverings of the plane by translates of K. In part I, we state results already known in this direction. In part II, we prove that ρK = (¼) ϑ(K) when K is strictly convex and in part III, we prove that ρK = (¼) ϑ(K) for all symmetric convex domains.

scholarly journals Dispersion for the wave equation inside strictly convex domains I: the Friedlander model case

2014 ◽  
Vol 180 (1) ◽  
pp. 323-380 ◽  
Author(s):  
Oana Ivanovici ◽  
Gilles Lebeau ◽  
Fabrice Planchon
Keyword(s):  
Wave Equation ◽  
Convex Domains ◽  
Model Case ◽  
Strictly Convex

scholarly journals A symmetry result for strictly convex domains

Analysis ◽  
2015 ◽  
Vol 35 (1) ◽  
Author(s):  
Alexander G. Ramm
Keyword(s):  
Convex Domains ◽  
Strictly Convex ◽  
Symmetry Result

AbstractLet

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