Monotonicity and its analytic and geometric implications
Author(s)Colding, Tobias; Minicozzi, William
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In this expository article, we discuss various monotonicity formulas for parabolic and elliptic operators and explain how the analysis of function spaces and the geometry of the underlining spaces are intertwined. After briefly discussing some of the well-known analytical applications of monotonicity for parabolic operators, we turn to their elliptic counterparts, their geometric meaning, and some geometric consequences.
DepartmentMassachusetts Institute of Technology. Department of Mathematics
Proceedings of the National Academy of Sciences of the United States of America
National Academy of Sciences (U.S.)
Colding, T. H., and W. P. Minicozzi. “Monotonicity and Its Analytic and Geometric Implications.” Proceedings of the National Academy of Sciences (2012).
Final published version