TL;DR
This paper investigates the number of ends on shrinkers by applying geometric covering methods, establishing polynomial growth bounds and finiteness results under volume conditions, with discussions on special cases.
Contribution
It introduces a geometric covering approach to analyze ends on shrinkers, providing new bounds and finiteness results not previously established.
Findings
Number of ends on any complete non-compact shrinker has polynomial growth bound.
Shrinkers with certain volume conditions have finitely many ends.
Discussion of special cases of shrinkers.
Abstract
In this paper we apply a geometric covering method to study the number of ends on shrinkers. On one hand, we prove that the number of ends on any complete non-compact shrinker is at most polynomial growth with fixed degree. On the other hand, we prove that any complete non-compact shrinker with certain volume comparison condition has finitely many ends. Some special cases of shrinkers are also discussed.
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Taxonomy
TopicsMathematical Dynamics and Fractals · Point processes and geometric inequalities · Stochastic processes and statistical mechanics