Showing papers in "American Mathematical Monthly in 1968"
2,100 citations
1,859 citations
1,113 citations
987 citations
580 citations
TL;DR: The Seminar on Atiyah-Singer Index Theorem (AM-57) as discussed by the authors was the first attempt to apply the AtiyahSinger Theorem to the Seminar.
Abstract: The description for this book, Seminar on Atiyah-Singer Index Theorem. (AM-57), will be forthcoming.
515 citations
237 citations
187 citations
176 citations
TL;DR: In this paper, the skeletal pair of a closed subset of the Euclidean plane is associated with a convex deficiency D and its skeletal pair (S,q), and it is shown that different sets have the same skeletal pair iff they have a similar deficiency.
Abstract: : To every closed subset A of the Euclidean plane is associated its convex deficiency D and its skeletal pair (S,q). Extending a known result (A is convex iff S = phi iff D = phi) one can prove: different sets have the same skeletal pair iff they have the same convex deficiency. Several other results are presented concerning the correspondence A approaching (S,q) and the properties of S and q. The relevance of these notions and theorems for a mathematical model of visual perception is emphasized. (Author)
TL;DR: The Problem of Apollonius as discussed by the authors has been studied extensively in the literature, see, e.g., The American Mathematical Monthly: Vol. 75, No. 1, pp. 5-15.
Abstract: (1968). The Problem of Apollonius. The American Mathematical Monthly: Vol. 75, No. 1, pp. 5-15.
TL;DR: The phenomena of least area problems Integration of differential forms over rectifiable sets Varifolds Variational problems involving varifolds References Additional references Index as discussed by the authors and Table 1 : A.
Abstract: The phenomena of least area problems Integration of differential forms over rectifiable sets Varifolds Variational problems involving varifolds References Additional references Index.
[...]
TL;DR: A Proof of Minkowski's Inequality for Convex Curves The American Mathematical Monthly: Vol 75, No 6, Vol 6, pp 581-593 as mentioned in this paper.
Abstract: (1968) A Proof of Minkowski's Inequality for Convex Curves The American Mathematical Monthly: Vol 75, No 6, pp 581-593
TL;DR: A simple proof of the Denjoy-Carleman theorem is given in this paper. But it is not a simple proof, and it cannot be found in the full version of this paper.
Abstract: (1968). A Simple Proof of the Denjoy-Carleman Theorem. The American Mathematical Monthly: Vol. 75, No. 1, pp. 26-31.