Existing cross domain recommender systems typically assume homogeneous user preferences across multiple domains to capture similarities of user-item interactions and to provide cross domain recommendations accordingly. Meanwhile, the heterogeneity of user behaviors is usually not well studied and captured during the recommendation process, where users might have vastly different interests in different domains. In addition, previous models focus primarily on recommendation tasks between domain pairs, and cannot be naturally extended to serve for multiple domain recommendation applications. To address these challenges, we propose to utilize the idea of adversarial learning to intelligently incorporate global user preferences and domain-specific user preferences for providing satisfying cross domain recommendations. In particular, our proposed Adversarial Cross Domain Recommendation (ACDR) model first obtains the latent representations of global user preferences from their explicit feature information, and then transforms them into domain-specific user embeddings, where we take into account user behaviors and their heterogeneous preferences among different domains. By doing so, we address the differences among user representations in the domain-specific latent space while also preserving global user preferences, as we effectively segment the distributions of domain-specific user embeddings in the shared latent space. The convergence of our proposed model is theoretically guaranteed. The proposed ACDR model leads to significant and consistent improvements in cross domain recommendation performance over the state-of-the-art baseline models, which we demonstrate through extensive experiments on three real-world datasets. In addition, we show that the improvements are greater on those datasets that are smaller and more sparse, on those users that have fewer interaction records in the dataset, and when user interactions from more product domains are included in the cross domain recommendation model.