Abstract
Several theorems go by this name. The present note adds to the assortment an unusual variant (Theorem 1), which involves the shape of the underlying region in an interesting way. We work in Euclidean spaces, although Lemma 2 and the second inequality of Lemma 3 carry over to general Riemannian manifolds. V and I I denote gradient and norm with respect to the standard inner product , and d stands for boundary. All our functions are real-valued. A gradient curve of a function f is an integral curve of Vf.
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