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6: Paper Source PDF document

Paper's Title:

Linearly Transformable Minimal Surfaces

Author(s):

Harold R. Parks and Walter B. Woods

Department of Mathematics, Oregon State University,
Corvallis, Oregon 97331--4605,
USA
parks@math.oregonstate.edu
URL
: http://www.math.oregonstate.edu/people/view/parks/

Abstract:

We give a complete description of a nonplanar minimal surface in R3 with the surprising property that the surface remains minimal after mapping by a linear transformation that dilates by three distinct factors in three orthogonal directions. The surface is defined in closed form using Jacobi elliptic functions.



6: Paper Source PDF document

Paper's Title:

Purely Unrectifiable Sets with Large Projections

Author(s):

Harold R. Parks

Department of Mathematics, Oregon State University,
Corvallis, Oregon 97331--4605,
USA
parks@math.oregonstate.edu
URL
: http://www.math.oregonstate.edu/people/view/parks/

Abstract:

For n2, we give a construction of a compact subset of that is dispersed enough that it is purely unrectifiable, but that nonetheless has an orthogonal projection that hits every point of an (n-1)-dimensional unit cube. Moreover, this subset has the additional surprising property that the orthogonal projection onto any straight line in is a set of positive 1-dimensional Hausdorff measure.


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