I want to develop a mobile application that is cross platform with good performance and design. Which technology should I use ?

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Either React Native or Flutter. I find developers for small businesses and startups, and those two are what I usually recommend to my clients. If you're going to do a web application in addition to mobile, I'd lean in favor of React Native over Flutter since you can do some common interface stuff with React. In terms of benchmarking, Flutter is usually faster than React Native, but in most cases either solution should work just fine.

I believe that Xamarin is the most complete cross-platform mobile app development framework, while .NET is an ideal development platform for the same.
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I'd react-native anytime. It is easy to learn for devs, has a lot of resources online, and when it comes to delivery, it supports iOS and Android both. If you're in an early-stage company, react-native also helps you keep the costing low as possible, as compared to running 2 different teams and 2 different tech stacks for your mobile. We help our clients on building and scaling apps., reach out to me on how FirstPrinciples.io can help you develop your world-class app in a cost-effective way. If you're looking out for a cheaper solution, I'd suggest hiring a react-native developer from Upwork. Cheers.,

Assuming that this is not a "fun only" project and you have some broader professional and financial goals that you want to achieve with this app...

For the best answer, let's clarify and map out the circumstances of your question:
1. Who will be your client (who pays for your solution), and what kind of technological requirements they have?
2. Will you develop and also maintain/update the app? How frequently do you plan to roll out fixes, updates?
3. Who will be the users of your app? And how large will be your user base? What will be their preferences in using the app? Are there any specific
...

From all my venture building experience I learned, that even questions that seem purely technology-related, it' best to start with such high-level questions. Once you know all your preferences and requirements, it will be much easier to decide which technology stack will serve you best.

And if you did not yet decide on these high-level questions, then apply the startup studio framework. Because that will help you to discover a lot more hidden opportunities and potentials.