Yang-Hui He

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1,500 appearances 1 recordings 1 series first heard Jan 2025 last heard Jan 2025

Yang-Hui He’s voice in public audio — every appearance, attributed to the second.

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So all of a sudden these th things are no longer two-dimensional real orientable surfaces.

But one complex dimensional what it's now called curves.

I mean it's a terrible name.

So a complex curve is actually a two-real dimensional surface.

And it turns out that all complex curves are orientable.

So you that you oh you already rule out things like you know Klein bottles and stuff like that or or Moerbius strips.

Yeah.

So the the com the complex structure requires orientability.

And that's partly because of Cauchy Riemann relations.

You know, you it puts a it puts a direction.

You can't get you can't get away.

But the idea is the the interesting thing is all of this now should be thought of as one

They're called curves because they're one complex dimension.

But they're not curves, right?

They're surfaces in the real sense.

Right?

So now here here comes so if you apply this to get to to the Gauss thing, this y you get this amazing trichotomy theorem.

And the theorem says

If you do this to our to the curvature, you can see this.

I mean this the number here is two, right?

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