Title: How to Generalize The Triangle Inequality to Higher Dimensions?
Abstract: The triangle inequality says two rays are length-minimizing if they form a straight line. What happens when rays become higher-dimensional geometric objects (cones)? This talk explores two generalizations: Lawlor's angle criterion for pairs of half-dimensional planes, and the appearance of singular area-minimizing cones in high dimensions. One intuition here is that the higher the dimensions, the less rigid are volume minimizers. Concepts/intuitions mentioned may include calibrated geometry and the concentration of measure.
Note: The talk will start at 4:10 pm
Daniel Mallory
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