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Minimal unfolded regions of a convex hull and parallel bodies
- Source :
- Hokkaido Math. J. 44, no. 2 (2015), 175-183
- Publication Year :
- 2012
- Publisher :
- arXiv, 2012.
-
Abstract
- The {\em minimal unfolded region} (or the {\em heart}) of a bounded subset $\Om$ in the Euclidean space is a subset of the convex hull of $\Om$ the definition of which is based on reflections in hyperplanes. It was introduced to restrict the location of the points that give extreme values of certain functions, such as potentials whose kernels are monotone functions of the distance, and solutions of differential equations to which Aleksandrov's reflection principle can be applied. %the temperature of a heat conductor with some initial-boundary condition, in which case the points are called the hot spots. We show that the minimal unfolded regions of the convex hull and parallel bodies of $\Om$ are both included in that of $\Om$.<br />Comment: to appear in Hokkaido Math. J
- Subjects :
- Convex hull
potential
Euclidean space
General Mathematics
52A40
31C12
Metric Geometry (math.MG)
heart
parallel body
Minimal unfolded region
convex body
Combinatorics
51F99
Monotone polygon
51M16, 51F99, 31C12, 52A40
Mathematics - Metric Geometry
hot spot
Bounded function
Classi cation
FOS: Mathematics
Convex body
Extreme value theory
51M16
Mathematics
Subjects
Details
- Database :
- OpenAIRE
- Journal :
- Hokkaido Math. J. 44, no. 2 (2015), 175-183
- Accession number :
- edsair.doi.dedup.....b0769008690da1c5da38b468c6840f02
- Full Text :
- https://doi.org/10.48550/arxiv.1205.0662