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Conformal invariance of harmonicity
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Mathematics
Area of mathematics
Analysis
Complex analysis
Riemann surfaces
Harmonic function on a Riemann surface
Created
2026-09-24
Updated
2026-09-24
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Under
a
holomorphic coordinate change
w
=
w
(
z
)
,
Δ
z
(
H
∘
w
)
=
∣
w
′
(
z
)
∣
2
(
Δ
w
H
)
∘
w
,
(1)
so the condition
Δ
H
=
0
is independent of the holomorphic
chart
.
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(7)
Harmonic function on a Riemann surface
Riemann surfaces
Complex analysis
Analysis
Area of mathematics
Mathematics
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