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2 votes
0 answers
48 views

Maximum coverage of an orthogonal polygon using $k$ rectangles

I have an orthogonal polygon (all edges are horizontal or vertical) which is convex (no holes in any row of column of the polygon). I would like to cover as much as possible of this orthogonal polygon ...
user536106's user avatar
1 vote
1 answer
158 views

Effect of snowflaking on doubling constants

This question is related to this one. Let $(X,d)$ be a metric space, let $\epsilon\in [0,1)$ and consider the snowflake $(X,d^{1-\epsilon})$. Suppose that $(X,d)$ has a finite doubling constant, ...
ABIM's user avatar
  • 5,405
1 vote
1 answer
428 views

Growth rate of bounded Lipschitz functions on compact finite-dimensional space

Let $\mathcal X$ be a metric space of diameter $D$ and "dimension" (e.g doubling dimension) $d$. Let $L \in [0, \infty]$ and $M \in [0, \infty)$ and consider the class $\mathcal H_{M,L}$ of $L$-...
dohmatob's user avatar
  • 6,853
5 votes
1 answer
547 views

Cover of a n-simplex with balls

Consider a n-simplex. For each edge (i,j), consider a n-ball, such that vertices i and j are antipodal on this ball. Is the simplex covered by the union of these balls? Thank you.
Max's user avatar
  • 195