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RESEARCH PRODUCT

Surfaces with Boundary

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One of the objectives of this book is to obtain a rigorous proof of a version of Green’s formula for compact subsets of \(\mathbb{R}^2\) whose topological boundary is a regular curve of class C 2. These sets are typical examples of what we will call regular 2-surfaces with boundary in \(\mathbb{R}^2\). The analogous three-dimensional example would consist of a compact set of \(\mathbb{R}^3\) whose topological boundary is a regular surface of class C 2. The following example is perhaps instructive.