I need a explanation on what does it mean to say a boundary is $C^k$. Can anyone help me please.
And also need some explanation on how to straighten boundary ?
What does it mean to say a boundary is $C^k$?
2
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analysis
differential-geometry
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0Well, I can explain it to you but I can't guarantee it'll be a "nice" explanation. – 2012-05-28
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0Roughly speaking, it means that locally the boundary behave like the graph of a $C^k$ function. – 2012-05-28
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0@Gigili Please do so , i want to understand . Thanks – 2012-05-28
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0How much differential geometry do you know? Do you know what a manifold is? – 2012-05-28
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0@Ananda: [This](http://en.wikipedia.org/wiki/Simplicial_homology#Definition) might help. – 2012-05-28
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0@N.I I can learn it , you can give your explanation :) – 2012-05-28
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2@Ananda: To not beat around the bush, I think that people are pointing out that your demanding a 'nice' explanation rubs some people the wrong way. In general, this question feels as though you're ordering others around, which does not make me want to write an answer. We also have no idea what your background is. Really - how much differential geometry do you know? In what context is this question coming up? If you put more into your question, I'm sure more people will be willing to answer it. – 2012-05-28
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0@mixedmath: sorry for posing question in such a way. I will edit the question. I know very less of differential geometry . But i am trying to learn this text : http://www.thehcmr.org/issue1_2/poincare_lemma.pdf . – 2012-05-28