| 提要文摘： | This book is intended for the researchers engaged in fields of mathematics and graduate students for a quick overview on the subject of the geometric measure theory with emphases on various basic ideas, techniques and their applications in problems arising in calculus of variations, geometrical analysis and nonlinear partial differential equations. The contents of the book mainly consist of the Hausdoff measure and its applications, Lipschitz functions rectifiable sets, the area and coarea formulae, BV functions and sets of the finite perimeter, Varifolds theory, and current theory. The present text also contains many concrete examples illustrating how the basic ideas and powerful techniques in geometric measure theory are applied. |
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