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It is well-known that galaxy environment has a fundamental effect in shapingits properties. We study the environmental effects on galaxy evolution, with anemphasis on the environment defined as the local number density of galaxies.The density field is estimated with different estimators (weighted adaptivekernel smoothing, 10$^{th}$ and 5$^{th}$ nearest neighbors, Voronoi andDelaunay tessellation) for a K$_{s}<$24 sample of $\sim$190,000 galaxies in theCOSMOS field at 0.1$<$z$<$3.1. The performance of each estimator is evaluatedwith extensive simulations. We show that overall, there is a good agreementbetween the estimated density fields using different methods over $\sim$2 dexin overdensity values. However, our simulations show that adaptive kernel andVoronoi tessellation outperform other methods. Using the Voronoi tessellationmethod, we assign surface densities to a mass complete sample of quiescent andstar-forming galaxies out to z$\sim$3. We show that at a fixed stellar mass,the median color of quiescent galaxies does not depend on their hostenvironment out to z$\sim$3. We find that the number and stellar mass densityof massive ($>$10$^{11}$M$_{\odot}$) star-forming galaxies have notsignificantly changed since z$\sim$3, regardless of their environment. However,for massive quiescent systems at lower redshifts (z$\lesssim$1.3), we find asignificant evolution in the number and stellar mass densities in denserenvironments compared to lower density regions. Our results suggest that therelation between stellar mass and local density is more fundamental than thecolor-density relation and that environment plays a significant role inquenching star formation activity in galaxies at z$\lesssim$1.

A Comparative Study of Density Field Estimation for Galaxies: New Insights into the Evolution of Galaxies with Environment in COSMOS out to z~3