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Monotonicity of half-plane capacity
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Probability theory
Stochastic process
Schramm–Loewner evolution
Compact H-hull
Mapping-out function of a compact H-hull
Half-plane capacity
2026-09-24
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If
compact H-hulls
satisfy
A
⊆
C
, then
hcap
(
A
)
≤
hcap
(
C
)
.
(1)
This follows from the
Brownian representation of half-plane capacity
or from composition of their mapping-out
functions
.
Ancestors
(10)
Half-plane capacity
Mapping-out function of a compact H-hull
Compact H-hull
Schramm–Loewner evolution
Stochastic process
Probability theory
Probability and statistics
Area of mathematics
Mathematics
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(1)
Past exam of the mathematics course of the University of Cambridge
/
2024
/
iii
/
Paper 203
/
1
/
b
/
i
/
Solution
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