WorldCat Identities

Toro, Tatiana 1964-

Works: 6 works in 19 publications in 1 language and 214 library holdings
Genres: Academic theses 
Roles: Author
Classifications: QA312, 515.42
Publication Timeline
Most widely held works by Tatiana Toro
Reifenberg parameterizations for sets with holes by Guy David( Book )

14 editions published between 2011 and 2012 in English and held by 208 WorldCat member libraries worldwide

Reifenberg parameterization of sets with holes by Guy David( Book )

1 edition published in 2012 in English and held by 2 WorldCat member libraries worldwide

On the geometry of rectifiable sets with Carleson and Poincaré-type conditions by Jessica Merhej( )

1 edition published in 2016 in English and held by 1 WorldCat member library worldwide

A central question in geometric measure theory is whether geometric properties of a set translate into analytical ones. In 1960, E.R. Reifenberg proved that if an n-dimensional subset M of Rn+d is well approximated by n-planes at every point and at every scale, then M is a locally bi-Hölder image of an n-plane. Since then, Reifenberg's theorem has been refined in several ways in order to ensure that M is a bi-Lipschitz image of an n-plane. In this thesis, we show that a Carleson condition on the oscillation of the tangent planes of an n-Ahlfors regular rectifiable subset M of Rn+d satisfying a Poincaré-type inequality is sufficient to prove that M is contained inside a bi-Lipschitz image of an n-dimensional affine subspace of Rn+d. We also show that this Poincaré-type inequality encodes geometrical information about M; namely it implies that M is quasiconvex
Functions in W², ²(R²) have Lipschitz graphs by Tatiana Toro( )

1 edition published in 1992 in English and held by 1 WorldCat member library worldwide

The geometry of uniform measures by Abdalla Dali Nimer( )

1 edition published in 2017 in English and held by 1 WorldCat member library worldwide

Uniform measures have played a fundamental role in geometric measure theory since they naturally appear as tangent objects. They were first studied in the groundbreaking work of Preiss where he proved that a Radon measure is n-rectifiable if and only if the n-density at almost every point of its support is positive and finite. However, very little is understood about them: for instance the only known n-uniform measures not supported on an affine n-plane were constructed by Preiss in 1987. In this thesis, we prove that the Hausdorff dimension of the singular set of any $n$-uniform measure is at most n-3. Then we characterize 3-uniform measures with dilation invariant support and construct an infinite family of 3-uniform measures all distinct and non-isometric, one of which is the Preiss cone
Local set approximation : infinitesimal to local theorems and applications / Stephen Lewis by Stephen Lewis( )

1 edition published in 2014 in English and held by 1 WorldCat member library worldwide

In this thesis we develop the theory of Local Set Approximation (LSA), a framework which arises naturally from the study of sets with singularities. That is, we describe the local structure of a set A in Euclidean space through studying a class of sets S which approximates A well in small balls. We will give two interpretations LSA in Chapters 2 and 3. If in small balls B(x; r), our set A is close to some nice model set S, the approximation is unilateral. On the other hand, if in small balls B(x; r), our set A is close to S and S is close to A, the approximation is bilateral. Both of these models appear naturally in areas of geometric measure theory such as area minimizers, mass minimizers, free boundary, and regularity of measures. In Chapters 4 and 5, we give applications of local set approximation to the study of asymptotically optimally doubling measures
Audience Level
Audience Level
  Kids General Special  
Audience level: 0.67 (from 0.67 for Reifenberg ... to 0.98 for Reifenberg ...)

Alternative Names
Tatiana Toro Colombiaans wiskundige

Tatiana Toro Colombian–American mathematician

Tatiana Toro mathématicienne colombienne-américaine

English (19)