Isabel Fernandez

Harmonic maps and constant mean curvature surfaces in H 2 x R

We introduce a hyperbolic Gauss map into the Poincar´e disk for any surface in H2×R with regular vertical projection, and prove that if the surface has constant mean curvature H = 1/2, this hyperbolic Gauss map is harmonic. Conversely, we show that every nowhere conformal harmonic map from an open simply connected Riemann surface Σ into the Poincaré disk is the hyperbolic Gauss map of a two-parameter family of such surfaces. As an application we obtain that any holomorphic quadratic differential on Σ can be realized as the Abresch-Rosenberg holomorphic differential of some, and generically infinitely many, complete surfaces with H = 1/2 in H2 x R. A similar result applies to minimal surfaces in the Heisenberg group Nil3. Finally, we classify all complete minimal vertical graphs in H2 × R.

Dietary nucleotides correct plasma and liver microsomal fatty acid alterations in rats with liver cirrhosis induced by oral intake of thioacetamide

BACKGROUND/AIMS Dietary nucleotides modulate a number of metabolic processes, including long-chain polyunsaturated fatty acid metabolism. In this study, we evaluated the effect of dietary nucleotides on plasma and liver microsomal fatty acid profiles in a rat model of liver cirrhosis induced by oral intake of thioacetamide. METHODS Fifty-four female Wistar rats were assigned to one of the following groups: rats in the thioacetamide group (n=45) were given 300 mg thioacetamide/l in their drinking water for 4 months, and rats in the control group (n=9) received water during the same period. After 4 months of treatment, 9 rats in each group were killed. The remaining rats in the thioacetamide group were divided into two new groups, and the animals in each were allowed to recover for 1 or 2 weeks on either a nucleotide-free diet or the same diet supplemented with 50 mg of each of the following: AMP, GMP, CMP, IMP and UMP per 100 g diet. RESULTS Saturated (mainly stearic acid), monounsaturated, and n-6 long-chain polyunsaturated fatty acids (mainly arachidonic acid), and also the unsaturation index decreased in plasma of rats with experimental cirrhosis. Administration of the diet supplemented with nucleotides to thioacetamide-treated rats corrected plasma levels of saturated, n-6 long-chain polyunsaturated fatty acids and the unsaturation index. In liver microsomes, the cirrhotic rats showed lower levels of protein and higher levels of palmitic, oleic, linoleic and arachidonic acids. Protein concentrations and levels of all the above-mentioned fatty acids were corrected with the nucleotide-enriched diet. CONCLUSIONS Dietary nucleotides contribute to correcting plasma and liver microsomal fatty acid alterations in rats with liver cirrhosis induced by chronic oral administration of thioacetamide.

Holomorphic quadratic differentials and the Bernstein problem in Heisenberg space

We classify the entire minimal vertical graphs in the Heisenberg group Nil 3 endowed with a Riemannian left-invariant metric. This classification, which provides a solution to the Bernstein problem in Nil 3 , is given in terms of the Abresch-Rosenberg holomorphic differential for minimal surfaces in Nil 3 .

Dietary Long-Chain Polyunsaturated Fatty Acids Influence the Recovery of Thioacetamide-Induced Liver Cirrhosis in Rats

BACKGROUND The aim of this study was to evaluate the dietary supplementation with omega-3 and omega-6 long-chain polyunsaturated fatty acids on the fatty acid composition of plasma and red blood cell membranes in rats with thioacetamide-induced liver cirrhosis. METHODS Thirty-eight female Wistar rats were given 300 mg thioacetamide/L in drinking water for 4 months to induce the experimental liver cirrhosis. Sixteen rats were used as controls. After treatment with thioacetamide, nine rats of each group were killed. Then, thioacetamide-treated rats were divided into three new groups, each receiving a different diet for 2 weeks: a semipurified diet (n = 9), the same diet supplemented with omega-3 long-chain polyunsaturated fatty acids (n = 10), or the same semipurified diet supplemented with omega-3 and omega-6 long-chain polyunsaturated fatty acids simultaneously (n = 10). The remaining control rats were fed the semipurified diet. Liver histology and plasma and erythrocyte fatty acid composition were assessed. RESULTS An apparent improvement of the histological damage took place in the rats fed the omega-3+ omega-6-supplemented diet. The diet supplemented with polyunsaturated fatty acids of the omega-3 series induced increases in the omega-3 long-chain polyunsaturated fatty acid levels in total plasma lipids, plasma lipid fractions and in erythrocyte phospholipids, and decreases in omega-6 long-chain polyunsaturated fatty acids in erythrocyte phospholipids during the recovery of rats with thioacetamide-induced liver cirrhosis. The administration of the diet supplemented with both omega-3 and omega-6 long-chain polyunsaturated fatty acids contributed to increase the levels of total plasma saturated, monounsaturated, and omega-6 long-chain polyunsaturated fatty acids from cirrhotic rats. CONCLUSION We conclude that the simultaneous supply of long-chain fatty acids of the omega-3 and the omega-6 series can be beneficial to improve the fatty acid status of this experimental model of liver cirrhosis.

Constant Mean Curvature Surfaces in 3-dimensional Thurston Geometries

This is a survey on the global theory of constant mean curvature surfaces in Riemannian homogeneous 3-manifolds. These ambient 3-manifolds include the eight canonical Thurston 3-dimensional geometries, i.e. R3, H3, S3, H2 \times R, S2 \times R, the Heisenberg space Nil3, the universal cover of PSL2(R) and the Lie group Sol3. We will focus on the problems of classifying compact CMC surfaces and entire CMC graphs in these spaces. A collection of important open problems of the theory is also presented.

Influence of administration of long-chain polyunsaturated fatty acids on process of histological recovery in liver cirrhosis produced by oral intake of thioacetamide.

Patients with liver cirrhosis frequently show some degree of protein-energy malnutrition and obviously require nutritional support. In this study, the treatment of rats consisted of thead libitum oral intake of a 300 mg/liter thioacetamide solution, used as drinking water for four months. Thioacetamide treatment produced a severe alteration in the plasma fatty acid profile with significant decreases of these, which mimicked changes described in human cirrhosis. This hepatotoxic agent causes nodular cirrhosis, with loss of the normal architecture of the liver and disruption of the vascular pattern. The goal of the study was to evaluate the influence of n-3 and n-6 series long-chain polyunsaturated fatty acid dietary supplementation in experimental animals and to assess the effects of those dietary components on structural recovery in the liver. Significant increases of saturated and monounsaturated fatty acids as well as n-6 polyunsaturated fatty acids were seen only in the animals given the n-6 polyunsaturated fatty acid supplemented diet. However, only rats given the standard diet exhibited some degree of histological regeneration.

A Hopf theorem for open surfaces in product spaces

Hopf’s theorem has been recently extended to compact genus zero surfaces with constant mean curvature H in a product space \( \mathcal{M}^2_k \, X \, \mathbb{R}\,where\,\mathcal{M}^2_k \) is a surface with constant Gaussian curvature \( k \,\neq\, 0 \, {\rm{[AbRo]}}\). It also has been observed that, rather than H = const., it suffices to assume that the differential dH of His appropriately bounded [AdCT]. Here, we consider the case of simply-connected open surfaces with boundary in \( \mathcal{M}^2_k \, X \, \mathbb{R}\,{\rm{such \, that}} \,dH \) is appropriately bounded and certain conditions on the boundary are satisfied, and show that such surfaces can all be described.